• J. Math. Chem. (IF 1.81) Pub Date : 2020-01-14
Alexander B. Doktorov, Alexander A. Kipriyanov

Abstract Theoretical investigation of exciplex generation under X-ray irradiation of the reacting system of non-polar solutions is consistently performed. The scheme of multistage reaction of ion-radical pairs generated under X-ray irradiation is improved as compared to that proposed in the literature previously. The possibility of excited state of electron donor formation, as well as additional channel of exciplex generation is taken into account. Formulation of the modified multistage process of exciplex generation in the framework of the theoretical approach of “effective particles” allows consistent derivation of the kinetic equations for the mean concentrations of reactants and on their basis calculation of the quantum yield of luminescence. Computations predict the change of exciplex generation efficiency under X-ray irradiation in comparison with the reaction under optical excitation. General properties of inhomogeneous sources of the obtained kinetic equations are established. A special case of the absence of excited donor generation is considered in detail, as well as the dependence of the studied values on the concentration of the electronic donor with some model simplifications.

更新日期：2020-01-15
• J. Math. Chem. (IF 1.81) Pub Date : 2020-01-03
Xing Tong, T. E. Simos

A new FinitDiff ($$=$$ Finite Difference) procedure is obtained for the efficacious solution of the DiffEquns ($$=$$ Differential Equations) in quantum chemistry.

更新日期：2020-01-04
• J. Math. Chem. (IF 1.81) Pub Date : 2020-01-02
P. Maroju, Á. A. Magreñán, Í. Sarría, Abhimanyu Kumar

This paper deal with the study of local convergence of fourth and fifth order iterative method for solving nonlinear equations in Banach spaces. Only the premise that the first order Fréchet derivative fulfills the Lipschitz continuity condition is needed. Under these conditions, a convergence theorem is established to study the existence and uniqueness regions for the solution for each method. The efficacy of our convergence study is shown solving various numerical examples as a nonlinear integral equation and calculating the radius of the convergence balls. We compare the radii of convergence balls and observe that by our approach, we get much larger balls as existing ones. In addition, we also include the real and complex dynamic study of one of the methods applied to a generic polynomial of order two.

更新日期：2020-01-02
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-26
Krishnan Balasubramanian

Abstract We have employed combinatorial techniques based on multinomial symmetric function (S-function) techniques for exhaustive enumeration and generation of relativistic (ω–ω states) states originating from relativistic 2-component molecular spinors for the seventh row superheavy dimers (Nh2-Ts2), transactinide dimers (Rf2-Rg2) and Ac2. The multinomial generators are so powerful that the complete set of relativistic states of all seventh row superheavy dimers or transactinide dimers are enumerated and constructed in a single generating function. We have computed and constructed the enumeration tables for all valence ω–ω states for the 7p-block and 6d-block dimers (Nh2-Ts2, Rf2-Rg2). Our results show that there are 6455 S-function terms giving rise to 102,830 valence ω–ω states- all arising only from the 6d shells of Bh2. Extension of the developed techniques to relativistic 4-component and 4-spinors arising from fermionic spin-3/2 particles are also suggested with potential applications NMR spectroscopy.

更新日期：2019-12-27
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-17
R. Akhrif, A. Kouibia, M. Pasadas

We present an approximation problem of surfaces of a generalized offset surface with offset variable distances and directions. Such approximating surface fits some given data points and minimizes a Sobolev’s semi-norm of order 3. The study of the new results, from a mathematical point of view, carefully establishing the proof of the convergence between the generalized offset surface and its approximating spline in an adequate parametric bicubic spline space. Moreover, the approximating spline function is computed and an estimation of the relative error is introduced. Finally, some numerical and graphic examples are shown in order to prove the useful and the effectiveness of our method.

更新日期：2019-12-18
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-17
Juan A. Rodríguez-Velázquez, Alexandru T. Balaban

Graph parameters and topological indices allow a discussion about hierarchical criteria for ranking monocyclic and polycyclic molecular (constitutional) chemical graphs. For brevity, chemical constitutional graphs will be referred to as CGs. These criteria include the number of vertices (graph order), cyclomatic numbers, vertex degrees (from one to four), number of polygons with increasing numbers of edges (3-, 4-, 5-gons, etc.), and vicinity with vertices of increasing rank. A similar hierarchy can be established for ranking vertices in a CG, and a detailed discussion is presented for ordering vertices in all seven identity CGs with 6 vertices and in 25 from the many identity CGs with 7 vertices. This is the first discussion of ranking the vertices of CGs from the viewpoint of centrality measures.

更新日期：2019-12-18
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-10
Wei Hua, Shi Xing Liu, Teng Zhang

The Bose–Einstein condensates in a harmonic trapping potential are studied numerically in one dimension by the symplectic method. The conservations of invariants are tested and the eigenvalues of different nonlinear coefficients are presented. Condensates with attractive two-body interaction and repulsive three-body interaction are investigated, and the interference and soliton behaviors of the condensates are discussed both in free space and in a harmonic trapping potential. It is demonstrated that the dynamic behaviors of condensates with attractive two-body interaction are quite different to those with repulsive two-body interactions, and the addition of a repulsive three-body interaction has significant effect on the stability of the state and the dynamical behavior of the system.

更新日期：2019-12-11
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-09
K. Aarthika, V. Shanthi, Higinio Ramos

This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction–convection–diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.

更新日期：2019-12-09
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-05
Walter Carballosa, Ana Granados, Domingo Pestana, Ana Portilla, José M. Sigarreta

The concepts of geometric–arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to obtain new inequalities involving the first Zagreb, the harmonic, and the geometric–arithmetic $$GA_1$$ indices. Furthermore, inequalities relating these indices and line graphs are proven.

更新日期：2019-12-06
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-05
Francisco I. Chicharro, Alicia Cordero, Tobías H. Martínez, Juan R. Torregrosa

The original version of this article unfortunately contained an error in title. Unintentionally, the special issue title was presented in addition to the article’s title.

更新日期：2019-12-05
• J. Math. Chem. (IF 1.81) Pub Date : 2019-12-04
Sheng Hao, T. E. Simos

A newly FinDiff ($$=$$ Finite Difference) process is developed for the productive application on the DifEquns ($$=$$ Differential Equations) in Chemistry.

更新日期：2019-12-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-30
S. Chandra Sekhara Rao, Sunil Kumar, Joginder Singh

We consider singularly perturbed parabolic reaction–diffusion problems of scalar and vector types. We construct a discrete Schwarz waveform relaxation method of higher order for their numerical solution. The method is shown to be parameter-uniformly convergent having almost fourth order in space and first order in time. Further, interesting result proven is much faster convergence of iterative process for small perturbation parameter. Numerical results demonstrating the efficiency of the proposed method and validating the theoretically proven convergence results are given.

更新日期：2019-11-30
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-27

Magnetic resonance spectroscopy (MRS), as a powerful and versatile diagnostic modality in physics, chemistry, medicine and other basic and applied sciences, depends critically upon reliable signal processing. It provides time signals by encoding, but cannot quantify on its own. Mathematical methods do so. The signal processor of choice for MRS is the fast Padé transform (FPT). The spectrum in the FPT is the unique polynomial quotient for the given Maclaurin expansion. The parametric FPT (parameter estimator) performs quantification of time signals encoded with MRS by explicitly solving the spectral analysis problem. Thus far, the non-parametric FPT (shape estimator) could not quantify. However, the non-parametric derivative fast Padé transform (dFPT) can quantify despite performing shape estimation alone. The dFPT was successfully benchmarked on synthesized MRS time signals for derivative orders ranging from 1 to 50. It simultaneously improved resolution (by splitting apart tightly overlapped peaks) and enhanced signal-to-noise ratio (by suppressing the background baseline). The same advantageous features of improving both resolution and signal-to-noise ratio are presently found to be upheld with encoded MRS time signals. Moreover, it is demonstrated that the dFPT hugely outperforms the derivative fast Fourier transform even for derivatives of orders as low as four. The clinical implications are discussed.

更新日期：2019-11-28
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-27
Marina Trapeznikova, Natalia Churbanova, Anastasia Lyupa

An explicit computational algorithm is developed to simulate complex flow of multiphase multicomponent slightly compressible fluid through porous media in view of heat sources. The proposed algorithm is based on the original model of porous media flow constructed by the analogy with the quasigasdynamic system of equations including the total energy conservation equation and modified to change the continuity equation type from parabolic to hyperbolic. It is approximated by a three-level explicit difference scheme having the second order of approximation in time and in space with a rather mild stability condition. The model takes into account gravitational and capillary forces, includes strongly nonlinear functions of the relative phase permeability. For the description of mass and energy transfer between the phases the model is generalized to account for multicomponent fluid structure. Conservation laws are formulated now for the components in terms of mass concentrations of components in the phases. The dependence of phase density and dynamic viscosity on pressure, temperature and multicomponent composition should be noted. Constants of the phase equilibrium close the system of equations. The created approach has been verified by test predictions of two- and three-phase fluid flows. Physically correct results were obtained, a good agreement with results by other authors was observed.

更新日期：2019-11-27
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-26
B. Datsko, M. Kutniv, A. Włoch

Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented.

更新日期：2019-11-27
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-26
Sasipim Putthikorn, Pornrat Ruengrot, Duangkamon Baowan

Self-assembling cyclic peptide nanotubes are widely investigated in many scientific fields due to many of their properties; controllable sizes, stable, and simple formation. In this research, the cyclic peptide nanotubes are modelled as the carriers to interact with a drug molecule. On employing the Lennard-Jones function and the continuous approximation, the energy value of the system can be evaluated. The main outcome of this research is a mathematical expression describing the relation of energy, radii of drug and peptide and the spacing between peptide units. We find that the drug is most stable when it is in the spacing between subunits of the peptide nanotubes. We also consider the energy behaviour of an offset drug inside three different sizes of the cyclic peptide nanotubes. We predict that the drug can be encapsulated inside the peptide nanotube when the difference of their radii is around 3 Å.

更新日期：2019-11-27
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-25

The collinear hydrogen exchange reaction is a paradigm system for understanding chemical reactions. It is the simplest imaginable atomic system with 2 degrees of freedom modeling a chemical reaction, yet it exhibits behaviour that is still not well understood—the reaction rate decreases as a function of energy beyond a critical value. Using lobe dynamics we show how invariant manifolds of unstable periodic orbits guide trajectories in phase space. From the structure of the invariant manifolds we deduce that insufficient transfer of energy between the degrees of freedom causes a reaction rate decrease. In physical terms this corresponds to the free hydrogen atom repelling the whole molecule instead of only one atom from the molecule. We further derive upper and lower bounds of the reaction rate, which are desirable for practical reasons.

更新日期：2019-11-26
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-25
Francisco I. Chicharro, Alicia Cordero, Tobías H. Martínez, Juan R. Torregrosa

The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods have been proposed in the literature. The evolution of these methods in terms of order of convergence implies the inclusion of a weight function for each case, showing an optimal fourth-order convergence, in the sense of Kung–Traub’s conjecture. The analysis of these new schemes is performed by means of complex dynamics. These methods are applied on the solution of the nonlinear Colebrook–White equation and the nonlinear system of the equilibrium conversion, both frequently used in Chemistry.

更新日期：2019-11-26
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-23
Krishnan Balasubramanian

Computational generating function techniques are outlined for combinatorics of colorings of all hyperplanes of the 6D-hypercube for 65 irreducible representations of the 6D-hyperoctahedral group isomorphic to the wreath product S6[S2] group of order 46,080. The computational techniques are inspired by a number of physico-chemical and biological applications to molecular chirality, molecular clusters, isomerization reaction graphs, relativistic effects, massively-large data sets, visualization, and genetic regulatory networks. Computational techniques are comprised of computing the generalized character cycle indices of 65 irreducible representations for all hyperplanes of the 6D-hypercube using the Möbius inversion technique followed by the construction of polynomial generators for different cycle types under the hyperoctahedral group action for all six types of hyperplanes of the 6D-hypercube. Subsequently, multinomial generating functions for colorings of all (6-q)-hyperplanes of the 6D-hypercube are constructed for q = 1 through 6. We have presented tables thus computed for the combinatorics for colorings of six hyperplanes of 6D-hypercube for 65 irreducible representations and outline applications to chemical and biological sciences.

更新日期：2019-11-26
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-23
Zsuzsanna É. Mihálka, Ádám Margócsy, Ágnes Szabados, Péter R. Surján

While variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this latter case, as we illustrate by sample numerical calculations, the points of the energy expectation value hypersurface where the eigenvalue equation is satisfied separate from those where the energy is stationary. We show that the variation of the energy at the eigensolution is determined by a generalized Hellmann–Feynman theorem. Functionals, other than the energy, can, however be constructed, that result the nonlinear Schrödinger equation upon setting their variation zero. The second centralized moment of the Hamiltonian is one example.

更新日期：2019-11-26
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-22
E. Urenda-Cázares, A. Gallegos, J. E. Macías-Díaz

In this paper, we propose a mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative to treatment of a glioma. The main idea is to incorporate the virotherapy after the first or second chemotherapy session using a specialist virus that attacks only tumor cells. Some simulations are presented. Based on the results, we conclude that with this combined therapy may reduce the number of chemotherapy sessions and may lead to obtain better results in the fight against gliomas.

更新日期：2019-11-26
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-21
A. Konguetsof

In the present research paper we propose a new generator of families of numerical methods with increasing number of internal layers in an attempt to achieve higher order accuracy. The intermediate stages consist of predictor-corrector methods. The final layer is a symmetric two step method with constant coefficients and also free parameters. Those parameters define each family of methods. At first the method is constructed with unknown parameters and subsequently their value is estimated in order to fulfill the requirement of maximum phase-lag order. The stability of the new numerical algorithm is analyzed and the local truncation error is computed. The generator of the new families is applied to well known problems and is found to be more efficient compared to other methods and numerical methods generators with similar characteristics, which attempt to numerically solve such problems.

更新日期：2019-11-21
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-20
L. Bayón, P. Fortuny Ayuso, J. M. Grau, M. M. Ruiz, P. M. Suárez

In this work, the Homotopy Perturbation method is used for the first time to solve an irreversible linear pathway with enzyme kinetics. The enzymatic system has Michaelis–Menten kinetics and is modeled by a system of nonlinear ordinary differential equations. The analytical solution obtained with the method allow us to optimize several objectives: minimal time to reach a certain percent of final product, minimal amount of enzymes employed in the process, or even multiple objective optimization via Pareto front. We present an example to demonstrate the results.

更新日期：2019-11-21
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-15
Ch. Tsitouras

A family of explicit, semi-symmetric, eighth-order, six-step methods for the numerical solution of $$y^{\prime \prime }=f(x,y)$$ is considered. This family can be derived through interpolation techniques and only two stages (function evaluations) are spent per step. A method is given with variable coefficients. This variance is based in the requirement to nullify the errors when solving the standard simple oscillator. We conclude with numerical tests over a set of problems justifying our effort of dealing with the new method.

更新日期：2019-11-17
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-13
M. G. Marmorino

A procedure is developed to generate rigorous rough upper bounds to radial moments [r2n] with integer n ≥ − 2 for the ground and excited states of atoms and molecules. These rough upper bounds to [r2n] enable the calculation of accurate upper and lower bounds to the lesser moment [rn] through existing and new formulas that utilize a lower bound to the square overlap of a trial function and true wave function (in this case through an energy lower bound via the Eckart formula). Error bars to [r−1], [r], [r2], and [r4] are calculated for the ground state of the non-relativistic infinite nuclear mass helium atom to yield expectation values within 0.037%, 0.018%, 0.039%, and 0.24% respectively, of the true values. As a byproduct of this investigation, a new formula for the error bar to observables is derived which is a slight improvement upon similar error bars. Also Lieb’s limit on the number of electrons that an atom can bind is reproduced.

更新日期：2019-11-14
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-08
P. Ghosh, J. F. Peters

This paper introduces an impulsive differential equation model useful in exploring the efficacy of activated charcoal in detoxifying a body suffering from methanol poisoning. Every year many individuals die due to methanol poisoning, mainly in the low income classes of the society. Among them, a large number of people die even before initial treatment. This work can provide a better knowledge on simple and inexpensive first aid to those affected individuals by administration of activated charcoal. Activated charcoal can be used as a universal antidote for many poisons because of its adsorbing ability. By using impulsive differential equations, we have studied the adsorption capacity of activated charcoal. Analytically we have shown the non-negativity, boundedness of the enzyme-methanol reaction model and emphasized on the formulation of absorption function for activated charcoal. The results obtained from analytical as well as numerical study give a basic idea of first aid within the general public and primary health centers, which can reduce the deaths caused by methanol poisoning in the long run.

更新日期：2019-11-11
• J. Math. Chem. (IF 1.81) Pub Date : 2019-11-05
Yu-Yu Ma, Chia-Liang Lin, T. E. Simos

A newly FD procedure is perused for the effective application on the DiffEqns in Chemical problems.

更新日期：2019-11-06
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-16
Hanlin Chen, Qiuzhi Guo

The Tutte poynomial T(G; x, y) of a graph G is a two-variable graph polynomial, and it gives interesting information about the graph. Many chemically interesting polycyclic polymers can be modeled by uniform or non-uniform polycyclic graphs. In this paper, we consider the Tutte poynomial of several classes of alternating polycyclic chains which contain phenylene chains and their dicyclobutadieno derivatives as special cases. Further, explicit closed formula of the number of spanning trees, the number of spanning forests and the number of spanning connected subgraphs of phenylenes (resp. the dicyclobutadieno derivatives of phenylenes) are obtained.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-09-18
M. G. Tokmachev, N. A. Tikhonov

Dynamics of deionization of electrolyte solution by sorption on aerogel electrodes is studied in the work on the basis of mathematical modeling. The processes of substance transfer by solution flow, diffusion and sorption in pores are taken into account. It is shown that for the correct description of the physical processes occurring in the deionizer under the potential difference on the electrode plates it is necessary to take into account the finite size of the hydrated ions and the change of the Stern layer on the surface of pores during substance diffusion. The change of the Stern layer is studied on the basis of mathematical modeling. The examples of simulation of the deionization process in a cyclic mode for different values of physical parameters are given.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-14
Marina A. Medvedeva, T. E. Simos

We research on the evolvent of newly FD process which can be applied efficiently on the DEs in Chemistry.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-09-19
Ramon Carbó-Dorca, Tanmoy Chakraborty

The present study deals with the possibility that N-dimensional hypercubes vertices could be constructed with chosen sets, composed by a given number of n elements. That is by: n-ary sets. Application of this possibility is discussed using as examples the coloring of graphs and the Erdös–Faber–Lovász conjecture, as well as protein and RNA descriptions. The outcome of this discussion induces a possibility to use p-dimensional hypercube vertices themselves as the possible elements of the n-ary sets as generators of N-dimensional hypercubes. Thus, providing: $$n = 2^{p}$$.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-17
F. R. R. Padilha, A. L. De Bortoli

Numerical simulations involving detailed kinetic combustion reaction mechanisms for long chain fuels are associated with prohibitive computational costs. Thus, there is the need for reduced kinetic mechanisms for the effective numerical simulation of these fuels. The objective of this work is the development of a skeletal mechanism of moderate stiffness for the methyl formate (MF). MF is not indicated as a biodiesel surrogate due to its very short chain, but its study allows to understand its role in the combustion process. Then, based on a detailed mechanism composed of 950 reactions and 176 species, Directed Relation Graph, Depth First Search and a model of Artificial Neural Networks are employed to obtain a skeletal mechanism with 43 reactions and 23 species. The results obtained are satisfactory.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-04
John C. Grifall-Sabo, Trenner Nolan, Matthew M. Beck, Christopher J. Barile

O2 reduction can occur via 1e−, 2e−, and 4e− pathways to yield O2−, H2O2, and H2O, respectively. Experimentally, it is often difficult to distinguish between the 1e− and 2e− pathways because O2− rapidly disproportionates in acidic and neutral aqueous solutions to H2O2 and O2. In this manuscript, we combine a mathematical model with previous experimental results with O2 reduction electrocatalysts on lipid-modified electrodes. The model demonstrates that for a typical O2 reduction catalyst, the individual rate constants for the 1e−, 2e−, and 4e− pathways can be determined within a fairly narrow range with O2 reduction current and H2O2 production rates as the only experimental inputs. This model will aid electrochemists in assessing the mechanism and selectivity of O2 reduction catalysts.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-31
Renato Lemus

An algebraic approach based on unitary algebras to calculate Franck–Condon factors (FCF’s) is presented. The method is based on the unitary group approach, which consists in adding a scalar boson to the $$\nu$$-D harmonic oscillator space, taking advantage of the transformation brackets connecting the energy, coordinate and momentum representations. In this scheme the solutions are given in terms of an expansion of harmonic oscillator functions. In this way the overlaps are expressed in terms of simple scalar product of the eigenvectors. As a benchmark to illustrate our approach the case of two 1D-Morse potentials is presented. Discussions concerned with both non-Condon contributions and the harmonic limit are included. FCF’s involving the 1D-Morse and asymmetric double Morse potentials are also considered. As an application, the FCF’s involving the S–S stretching in the $$\hbox {S}_2\hbox {O}$$ molecule are described in terms of two Morse potentials.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-10-29
Bryan S. Hernandez, Eduardo R. Mendoza, Aurelio A. de los Reyes V

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the “Multistationarity Algorithm for PLK systems” (MSA), combines (i) the extension of the “higher deficiency algorithm” of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg’s “deficiency one algorithm” to such systems.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-31
Ji-Huan He, Chang Sun

Thin film arises in various applications from electrochemistry to nano devices, many mathematical tools were adopted to study the problem, e.g. Lie symmetries and conservation laws, however, the variational approach is rare. This paper shows that the semi-inverse method is an effective approach to establishment of a variational formulation for the thin film equation. A detailed derivation process is given, a special skill for construction of a heuristic trial-functional is elucidated.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-06
Hiteshi Tandon, Tanmoy Chakraborty, Vandana Suhag

Knowledge of the nature of a chemical reactivity descriptor holds immense value to theoretical scientists. An appreciable number of works have been carried out in this realm. Polarizability (α) is one amongst such constructs. Fundamentally, it is a linear response of a systems electron cloud to an external applied electric field. The concept of polarizability is being widely adopted in the contemporary world of chemistry; however a suitable scale of measurement of atomic polarizability is still to be designed. In this work, an ansatz to compute atomic static dipole polarizability is proposed considering the conjoint action of absolute radius (r) and electronegativity (χ) for 103 elements of periodic table. We have evaluated the data invoking regression analysis. The computed data mirrors the periodicity remarkably satisfying all the sine qua non of a standard scale of polarizability. It presents an excellent quantitative correlation with ionization energy. Further, molecular polarizability (αm) is determined conceptualizing the property of additivity. A superior correlation between theoretical vis-à-vis existing molecular polarizabilities is observed.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-31
Genyuan Li

In the development of a new compound in chemistry and molecular biology, especially a new medicine in pharmaceutical industry, we often need to find candidate(s), a molecule or molecules, with the best desired property (e.g., binding affinity in medicine) from a large set of molecules with the same scaffold but m distinct functional substitutes at each of its n different sites. The total number $$N_{\mathrm{lib}}$$ of molecules in this library is $$m^n$$. In some cases, $$N_{\mathrm{lib}}$$ can be a very large number (e.g., millions). This is a challenging task because it is costly and often infeasible to synthesize and test all of these molecules. A new algorithm referred to as optimal sequential search is developed to overcome this difficulty. Especially, this algorithm is chemically intuitive which only uses the information of molecule composition, and accessible to practical chemists. The algorithm can be applied to small, medium and large size molecule libraries. With syntheses and property measurements for a limited number of molecules, the top best candidate molecules can be effectively captured from the whole library. Three examples with library size 64, 160,000 and 1,048,576, respectively, are used for illustration. For the first small library, syntheses and property measurements of 17 molecules are sufficient to capture the top 7 best candidate molecules; for the two medium and large libraries, syntheses and property measurements of about one thousand molecules can capture most or a large part of the top 500, especially the top 100 best candidate molecules. However, the algorithm needs to perform multiple (e.g., hundreds of) iterative syntheses and property measurements. The time cost may not be acceptable if the algorithm is performed manually. To make the algorithm practical, automation of the sequential searching process is the following task.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-31

Nuclear magnetic resonance spectroscopy originated in physics and quickly found versatile applications of paramount importance in other sciences, including chemistry. Signal processing in this methodology is a key to data analysis and interpretation. Herein, one of the most powerful tools from mathematical theory of approximations, known as rational polynomials, is the prime example of reliable handling of the two stumbling blocks that hamper further progress: noise suppression and resolution improvement. Within this realm resides the fast Padé transform (FPT), which simultaneously solves both these problems. It has a self-correcting procedure, which is automatically built in rational polynomials through noise suppression by pole-zero cancellations in spectra. Moreover, by solving the quantification problem (called spectral analysis in mathematics), the FPT can unequivocally separate overlapped peaks and thereby improve resolution. Further, lineshape estimations are provided by both non-parametric and parametric signal processing in the FPT. Since the FPT includes singularities (poles) of the expanded function, it achieves exponental convergence $$\exp {(-N)}$$ (the so-named spectral resolution) with respect to the size N of the basis set. This is contrasted to merely the inverse-power-law convergence 1 / N in the fast Fourier transform because its basis functions do not describe the singularities of the expanded function. The present investigation reports on practical aspects of all these critical features and gives several representative illustrations for measured time signals heavily contaminated with noise.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-24
Re-Bing Wu, Qiuyang Sun, Tak-san Ho, Herschel Rabitz

A general quantum system may be steered by a control of either classical or quantum nature and the latter scenario is particularly important in many quantum engineering problems including coherent feedback and reservoir engineering. In this paper, we consider a quantum system steered by a quantum controller and explore the underlying Q–Q (quantum–quantum) control landscape features for the expectation value of an arbitrary observable of the system, with the control being the engineered initial state of the quantum controller. It is shown that the Q–Q control landscape is inherently convex, and hence devoid of local suboptima. Distinct from the landscapes for quantum systems controlled by time-dependent classical fields, the controllability is not a prerequisite for the Q–Q landscape to be trap-free, and there are no saddle points that generally exist with a classical controller. However, the forms of Hamiltonian, the flexibility in choosing initial state of the controller, as well as the control duration, can influence the reachable optimal value on the landscape. Moreover, we show that the optimal solution of the Q–Q control landscape can be readily extracted from a de facto landscape observable playing the role of an effective “observer”. For illustration of the basic Q–Q landscape principles, we consider the Jaynes–Cummings model depicting a two-level atom in the presence of a cavity quantized radiation field.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-09-13
Junlai Qiu, Junjie Huang, T. E. Simos

Our research pays attention to the deployment of newly algorithm which is useful on quantum chemical problems.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-14
Xunying Zhang, T. E. Simos

We give attention to the evolvement of newly FD scheme for problems existed in Chemistry.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-07-02
Ji-Huan He, Fei-Yu Ji

Taylor series is accessible to all students and it is a useful mathematical tool to nonlinear equations. This paper shows it is extremely simple to solve approximately the well-known Lane–Emden equation.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-07-02
Qian Dong, Ariadna J. Torres-Arenas, Guo-Hua Sun, O. Camacho-Nieto, Smain Femmam, Shi-Hai Dong

We study quantum system with a symmetric sine hyperbolic type potential $$V(x)=V_{0}[\sinh ^4(x)-k\sinh ^2(x)]$$, which becomes single or double well depending on whether the potential parameter k is taken as negative or positive. We find that its exact solutions can be written as the confluent Heun functions $$H_{c}(\alpha , \beta , \gamma , \delta , \eta ; z)$$, in which the energy level E is involved inside the parameter $$\eta$$. The properties of the wave functions, which is strongly relevant for the potential parameter k, are illustrated for a given potential parameter $$V_{0}$$. It is shown that the wave functions are shrunk to the origin when the negative potential parameter |k| increases, while for a positive k which corresponding to a double well, the wave functions with a certain parity are changed sensitively.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-07-05
Valdas Laurinavičius, Feliksas Ivanauskas, Anatolij Nečiporenko

We analyze a mathematical model for drug delivery monitoring subject to flow-through bioreactor. We use a convection–diffusion–reaction model combined with PID control. Enzyme-containing bioreactor converts a prodrug into an active drug. This approach connects two aspects of drug delivery, mechanical pumps and prodrugs. Drug delivery monitoring is performed by adjusting the prodrug inflow pressure. We model several dynamic treatment regimes. A combined algorithm of treatment regimes can be used for personalized treatment. A control-aided system allows us to reduce the impact of pumping fluctuations, diffusion slowdown, and drug production rate reduction.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-08-01
Ji-Teng Jia

In recent years, a number of numerical algorithms of O(n) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an n-by-n cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at $$O(\log n)$$. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2019-07-01
Jorge E. Macías-Díaz

Departing from a two-dimensional hyperbolic system that describes the interaction between some activator and inhibitor substances in chemical reactions, we investigate a general form of that model using a finite-difference approach. The model under investigation is a nonlinear system consisting of two coupled partial differential equations with generalized reaction terms. The presence of two-dimensional diffusive terms consisting of fractional operators of the Riesz type is considered here, using spatial differentiation orders in the set $$(0 , 1) \cup (1 , 2]$$. We impose initial conditions on a closed and bounded rectangle, and a four-step fully explicit finite-difference methodology based on the use of fractional-order centered differences is proposed. Among the most important results of this work, we establish analytically the second-order consistency of our scheme. Moreover, a discrete form of the energy method is employed to prove the stability, the boundedness and the quadratic convergence of the technique. Some numerical simulations obtained through our method show the appearance of Turing patterns and wave instabilities, in agreement with some reports found in the literature on superdiffusive hyperbolic activator–inhibitor systems.

更新日期：2019-11-04
• J. Math. Chem. (IF 1.81) Pub Date : 2010-05-22
Matthew Hudelson

We expand on the work of Hosoya to describe a generalization of continued fractions called "tree expressions." Each rooted tree will be shown to correspond to a unique tree expression which can be evaluated as a rational number (not necessarily in lowest terms) whose numerator is equal to the Hosoya index of the entire tree and whose denominator is equal to the tree with the root deleted. In the development, we use Z(G) to define a natural candidate ζ(G, v) for a "vertex topological index" which is a value applied to each vertex of a graph, rather than a value assigned to the graph overall. Finally, we generalize the notion of tree expression to "labeled tree expressions" that correspond to labeled trees and show that such expressions can be evaluated as quotients of determinants of matrices that resemble adjacency matrices.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 1991-01-01
N Luo,M Shibata,R Rein

A systematic analysis is presented of the algorithm for converting a virtual-bond chain, defined by the coordinates of the alpha-carbons of a given protein, into a complete polypeptide backbone. An alternative algorithm, based upon the same set of geometric parameters used in the Purisima-Scheraga algorithm but with a different "linkage map" of the algorithmic procedures, is proposed. The global virtual-bond chain geometric constraints are more easily separable from the loal peptide geometric and energetic constraints derived from, for example, the Ramachandran criterion, within the framework of this approach.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2018-01-01

Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable amount of time and extracts another hydrogen atom from the molecule prior to dissociation. This phenomenon has been coined roaming and has since been reported in the dissociation of a number of other molecules. In this paper we investigate roaming in Chesnavich's CH 4 + model. During dissociation the free hydrogen must pass through three phase space bottleneck for the classical motion, that can be shown to exist due to unstable periodic orbits. None of these orbits is associated with saddle points of the potential energy surface and hence related to transition states in the usual sense. We explain how the intricate phase space geometry influences the shape and intersections of invariant manifolds that form separatrices, and establish the impact of these phase space structures on residence times and rotation numbers. Ultimately we use this knowledge to attribute the roaming phenomenon to particular heteroclinic intersections.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2011-01-01
Momchil Velkovsky,Rachel Snider,David E Cliffel,John P Wikswo

An analytic approach to the modeling of stop-flow amperometric measurements of cellular metabolism with thin glucose oxidase and lactate oxidase electrodes would provide a mechanistic understanding of the various factors that affect the measured signals. We divide the problem into two parts: (1) analytic formulas that provide the boundary conditions for the substrate and the hydrogen peroxide at the outer surface of the enzyme electrode layers and the electrode current expressed through these boundary conditions, and (2) a simple diffusion problem in the liquid compartment with the provided boundary conditions, which can be solved analytically or numerically, depending on the geometry of the compartment. The current in an amperometric stop-flow measurement of cellular glucose or lactate consumption/excretion is obtained analytically for two geometries, corresponding to devices developed at the Vanderbilt Institute for Integrative Biosystems Research and Education: a multianalyte nanophysiometer with effective one-dimensional diffusion and a multianalyte microphysiometer, for which plentiful data for metabolic changes in cells are available. The data are calibrated and fitted with the obtained time dependences to extract several cellular fluxes. We conclude that the analytical approach is applicable to a wide variety of measurement geometries and flow protocols.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2012-10-02
Shane L Hubler,Gheorghe Craciun

Biochemistry has many examples of linear chain polymers, i.e., molecules formed from a sequence of units from a finite set of possibilities; examples include proteins, RNA, single-stranded DNA, and paired DNA. In the field of mass spectrometry, it is useful to consider the idea of weighted alphabets, with a word inheriting weight from its letters. We describe the distribution of the mass of these words in terms of a simple recurrence relation, the general solution to that relation, and a canonical form that explicitly describes both the exponential form of this distribution and its periodic features, thus explaining a wave pattern that has been observed in protein mass databases. Further, we show that a pure exponential term dominates the distribution and that there is exactly one such purely exponential term. Finally, we illustrate the use of this theorem by describing a formula for the integer mass distribution of peptides and we compare our theoretical results with mass distributions of human and yeast peptides.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2012-05-01

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2015-02-14
Nils A Baas,Nadrian C Seeman,Andrew Stacey

We discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Furthermore, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2015-12-25
Mihaly Mezei

It is shown that the extent of deviation of a molecular shape from spherical can be characterized by comparing the distribution of the circular variances, a measure originally proposed to quantify angular spread, of the vectors from each atom to the rest of the molecule to the circular variance of a collection of atoms filling the unit sphere. Different measures for quantifying the difference between distribution are proposed and compared.

更新日期：2019-11-01
• J. Math. Chem. (IF 1.81) Pub Date : 2015-09-01
Robert Penfold,Peter J Wilde

The central idea observes a recursive mapping of [Formula: see text]-body intramolecular interactions to [Formula: see text]-body terms that is consistent with the molecular topology. Iterative application of the line graph transformation is identified as a natural and elegant tool to accomplish the recursion. The procedure readily generalizes to arbitrary [Formula: see text]-body potentials. In particular, the method yields a complete characterization of [Formula: see text]-body interactions. The hierarchical structure of atomic index lists for each interaction order [Formula: see text] is compactly expressed as a directed acyclic graph. A pseudo-code description of the generating algorithm is given. With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of [Formula: see text]-body interactions can be implemented straightforwardly to handle large bio-molecular systems. Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

更新日期：2019-11-01
Contents have been reproduced by permission of the publishers.

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