In this paper, we give a new approach to the representation of solutions to second order backward stochastic differential equations (2BSDEs). This approach ensures the wellposedness of 2BSDEs under an extended monotonicity condition which generalizes the usual monotonicity condition.

Let \({\mathcal{A}}\) and \({\mathcal{B}}\) be uniform algebras and p(z,w) = zmwn a twovariable monomial. We characterize maps T from certain subsets of \({\mathcal{A}}\) into \({\mathcal{B}}\) such that \(\sigma_{\pi}(p(T(f),T(g))) \subset \sigma_{\pi}(p(f,g))\) holds for all f and g in the domain of T; peripherally monomial-preserving maps. Furthermore \({\mathcal{A}}\) and \({\mathcal{B}}\) are

We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov process such that the level of performance of one component can change only for one level lower than the observed one, and the failures are independent for different

The first author introduced an integration theory of vector functions with respect to an operator-valued measure in complete bornological locally convex vector spaces. In this paper some important results behind this Dobrakov-type integration technique in non-metrizable spaces are given.

In the first part some conditions under which a permutation preserves Buck’s measure density, are derived. In the second part is constructed a countable system of permutations which has the ergodic property on the system of Buck’s measurable sets.

In this paper we show that if G is a group acting on a graph X with inversions such that G has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.

After a short introduction where a few main notions and results are recalled, we state some results connected with generated and L∞-type pseudoresolvents. Among others, we give theorems of characterization both for L∞-type pseudoresolvents and for their generators. The relation between L∞-type pseudoresolvents and C0-equicontinuous semigroups is also pointed out. The last part of the present paper

We investigate lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field ξ and whose screen distribution is integrable. We prove some results on parallel vector fields and on a leaf of the integrable distribution \(D_{0} \perp \langle\xi\rangle\) of this class. A theorem on a geometrical configuration of the screen distribution is obtained. We show that any totally

We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.

The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction a x2 + b x2/(1 + c x2) (a > 0, c > 0) are given by the confluent Heun functions Hc(α, β, γ, δ, η;z). The minimum value of the potential well is calculated as Vmin(x)=−(a+|b|−2a |b|)/c at x=±[(|b|/a−1)/c]1/2 (|b| > a) for the double-well case (b < 0). We illustrate the wave functions through varying the potential

Numerical results for the axially compressed cylindrical shell demonstrate the post-buckling response snaking in both the applied load and corresponding end-shortening. Fluctuations in load, associated with progressive axial formation of circumferential rings of dimples, are well known. Snaking in end-shortening, describing the evolution from a single dimple into the first complete ring of dimples

In this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account micro-inertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin’s Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures

Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thin-plate equation, present

This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also

A graph is ℓ-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting ℓ vertices. We prove that 3-regular graphs are 2-reconstructible.

Let R be a commutative ring and M an R-module. In this article, we introduce the concept of S-2-absorbing submodule. Suppose that S ⊆ R is a multiplicatively closed subset of R. A submodule P of M with (P :R M) ∩ S = ∅ is said to be an S-2-absorbing submodule if there exists an element s ∈ S and whenever abm ∈ P for some a, b ∈ R and m ∈ M, then sab ∈ (P :R M) or sam ∈ P or sbm ∈ P. Many examples,

We show how the full covering argument can be used to prove some type of Cauchy mean value theorem.

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compatible filter and 𝒜/ Θ (F). Moreover, a representation

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω:=Ω0\Ω¯1⊂𝕉N, N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric

In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given

In this paper we present limit theorems for lifetime distributions connected with network’s reliability as distributions of random variables(r.v.) min(Y1, Y2,..., YM) and max(Y1, Y2,..., YM ), where Y1, Y2,..., are independent, identically distributed random variables (i.i.d.r.v.), M being Power Series Distributed (PSD) r.v. independent of them and, at the same time, Yk, k = 1, 2, ..., being a sum

The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram–Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix

A plume model is used to describe the variation of the salt concentration at the discharge of a river into a saline water. The integral model of the plume behavior consists of a set of ordinary differential equations derived from conservation of mass, momentum and salt concentration. The temperatures of the plume and ambient saline water are considered equal. The concentration of the salt in the river

Let 𝒭 be a commutative ring with unity, 𝒜, 𝒝 be 𝒭-algebras, 𝒨 be (𝒜, 𝒝)-bimodule and 𝒩 be (𝒝, 𝒜)-bimodule. The 𝒭-algebra 𝒢 = 𝒢(𝒜, 𝒨, 𝒩, 𝒝) is a generalized matrix algebra defined by the Morita context (𝒜, 𝒝, 𝒨, 𝒩, ξ𝒨𝒩, Ω𝒩𝒨). In this article, we study Jordan σ-derivations on generalized matrix algebras.

We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di

The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p 5 elements (p a prime) and nilpotency index 4 are given. And the number and structure of γ-constacyclic codes over those rings, of length relatively prime to the characteristic of the residue field of the ring, are determined.

In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix D is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the

Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g1, . . ., gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr. We characterize the Hilbert functions of graded E–modules of the type F/M, with M graded submodule of F. The existence of a unique lexicographic submodule of F with the same Hilbert function

The expression of the structure equation of a mechanism is significant to present the last position of the mechanism. Moreover, in order to attain the constraint manifold of a chain, we need to constitute the structure equation. In this paper, we determine the structure equations and the constraint manifolds of a spherical open-chain in the Lorentz space. The structure equations of spherical open chain

In this paper, we establish sufficient criteria for the existence of solutions for a new kind of nonlinear Langevin equation involving conformable differential operators of different orders and equipped with integral boundary conditions. We apply the modern tools of functional analysis to derive the desired results for the problem at hand. Examples are constructed for the illustration of the obtained

In this paper, we show an energy convexity and thus uniqueness for weakly intrinsic bi-harmonic maps from the unit 4-ball B1⊂ℝ4 into the sphere 𝕊n. In particular, this yields a version of uniqueness of weakly harmonic maps on the unit 4-ball which is new. We also show a version of energy convexity along the intrinsic bi-harmonic map heat flow into 𝕊n, which in particular yields the long-time existence

Let P and Q be relatively prime integers greater than 1, and let f be a real valued discretely supported function on a finite dimensional real vector space V. We prove that if $f_{P}(x)=f(Px)-f(x)$ and $f_{Q}(x)=f(Qx)-f(x)$ are both $\Lambda $ -periodic for some lattice $\Lambda \subset V$ , then so is f (up to a modification at $0$ ). This result is used to prove a theorem on the arithmetic of elliptic

We study intersections of orbits in polynomial semigroup dynamics with lines on the affine plane over a number field, extending previous work of D. Ghioca, T. Tucker, and M. Zieve (2008).

The Cauchy problem of the 2D Zakharov–Kuznetsov equation ∂t⁡u+∂x⁡(∂x⁢x+∂y⁢y)⁡u+u⁢ux=0 is considered. It is shown that the 2D Z-K equation is locally well-posed in the endpoint Sobolev space H-1/4, and it is globally well-posed in H-1/4 with small initial data. In this paper, we mainly establish some new dyadic bilinear estimates to obtain the results, where the main novelty is to parametrize the singularity

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version

It has been recently discovered that in smooth unfoldings of maps with a rank-one homoclinic tangency there are codimension two laminations of maps with infinitely many sinks. Indeed, these laminations, called Newhouse laminations, occur also in the holomorphic context. In the space of polynomials of ℂ2, with bounded degree, there are Newhouse laminations.

We prove that the numerical invariant 3μ−4τ of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the curve is non-singular. This provides a new perspective to understand the question posed by Dimca and Greuel. Moreover, our work can be put in the general framework of discovering monotonic invariants under blowups.

In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection πλ,μ:V𝔸(λ)∨⊗𝔸V𝔸(μ)∨↠V𝔸(λ+μ)∨ sending the tensor product of the highest weight vectors to the highest weight vector in terms of convolution products. When the quiver Hecke algebra is symmetric and the base field

We consider integrable analytic deformations of codimension one holomorphic foliations near an initially singular point. Such deformations are of two possible types. The first type is given by an analytic family {Ωt}t∈D of integrable one-forms Ωt defined in a neighborhood U⊂ℂn of the initial singular point, and parametrized by the disc D⊂ℂ. The initial foliation is defined by Ω0. The second type, more

We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold (M,G,𝒥) with a Hamiltonian Killing

Let 𝔾 be a three-dimensional Lie group with a bi-invariant metric. Consider Ω⊂𝔾 a strictly convex domain in 𝔾. We prove that if Σ⊂Ω is a stable CMC free-boundary surface in Ω then Σ has genus either 0 or 1, and at most three boundary components. This result was proved by Nunes [I. Nunes, On stable constant mean curvature surfaces with free-boundary, Math. Z.287(1–2) (2017) 73–479] for the case where

We classify finite groups acting by birational transformations of a nontrivial Severi–Brauer surface over a field of characteristic zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism group of a smooth cubic surface over a field 𝕂 of characteristic zero that has no 𝕂-points is abelian, and find a sharp bound for the Jordan constants of birational

We introduce a new class of entire functions ℰ which consists of all F0∈𝒪(ℂ) for which there exists a sequence (Fn)∈𝒪(ℂ) and a sequence (λn)∈ℂ satisfying Fn(z)=λn+1eFn+1(z) for all n≥0. This new class is closed under the composition and it is dense in the space of all nonvanishing entire functions. We prove that every closed set V⊂ℂ containing the origin and at least one more point is the set of

We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L⁢(12,π⊗χ) for GL2×GL1 explicit, especially in terms of the usual conductor 𝐂⁢(πfin). There is no clue that the original choice, due to Michel and Venkatesh, of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some

Let G be a discrete group and 𝒞 be an additive spherical G-fusion category. We prove that the state sum 3-dimensional HQFT derived from 𝒞 is isomorphic to the surgery 3-dimensional HQFT derived from the G-center of 𝒞.

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net 𝒜 with central charge c=8k depends on the “gravitational anomaly” k(mod3). In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed Sn-categories arising from permutation

We develop, in the context of the boundary of a supercritical Galton–Watson tree, a uniform version of large deviation estimate on homogeneous trees to estimate almost surely and simultaneously the Hausdorff and packing dimensions of the Mandelbrot measure over a suitable set 𝒥. As an application, we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of a fractal set related

We provide the first nontrivial upper bound for the chemical distance exponent in two‐dimensional critical percolation. Specifically, we prove that the expected length of the shortest horizontal crossing path of a box of side length n in critical percolation on ℤ2 is bounded by Cn2 − δπ3(n) for some δ > 0, where π3(n) is the “three‐arm probability to distance n.” This implies that the ratio of this

We study the generalised Iwasawa invariants of ℤpd-extensions of a fixed number field K. Based on an inequality between ranks of finitely generated torsion ℤp⁢[[T1,…,Td]]-modules and their corresponding elementary modules, we prove that these invariants are locally maximal with respect to a suitable topology on the set of ℤpd-extensions of K, i.e., that the generalised Iwasawa invariants of a ℤpd-extension

Let X⊆ℙN be a non-degenerate normal projective variety of codimension e and degree d with isolated ℚ-Gorenstein singularities. We prove that the Castelnuovo–Mumford regularity reg(𝒪X)≤d−e, as predicted by the Eisenbud–Goto regularity conjecture. Such a bound fails for general projective varieties by a recent result of McCullough–Peeva. The main techniques are Noma’s classification of non-degenerate

In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form −div(𝒜(x,∇u))=μin Ω,u=0on ∂Ω, where μ is a finite signed Radon measure in Ω, Ω⊂ℝn is a bounded domain such that its complement ℝn∖Ω is uniformly p-thick and 𝒜 is a Carathéodory vector-valued function satisfying growth and monotonicity

We prove that the singularities of the R-matrix R(k) of the minimal quantization of the adjoint representation of the Yangian Y(𝔤) of a finite dimensional simple Lie algebra 𝔤 are the opposite of the roots of the monic polynomial p(k) entering in the OPE expansions of quantum fields of conformal weight 3/2 of the universal minimal affine W-algebra at level k attached to 𝔤.

In this note, we study the maximal perimeter of a convex set in ℝn with respect to various classes of measures. Firstly, we show that for a probability measure μ on ℝn, satisfying very mild assumptions, there exists a convex set of μ-perimeter at least CnVar|X|4𝔼|X|. This implies, in particular, that for any isotropic log-concave measure μ, one may find a convex set of μ-perimeter of order n18. Secondly

Let 𝓐 be a ⋆-algebra, δ : 𝓐 → 𝓐 be a linear map, and z ∈ 𝓐 be fixed. We consider the condition that δ satisfies xδ(y)⋆ + δ(x)y⋆ = δ(z) (x⋆δ(y) + δ(x)⋆y = δ(z)) whenever xy⋆ = z (x⋆y = z), and under several conditions on 𝓐, δ and z we characterize the structure of δ. In particular, we prove that if 𝓐 is a Banach ⋆-algebra, δ is a continuous linear map, and z is a left (right) separating point

Let X be a completely regular topological space. For each closed non-vanishing ideal H of CB(X), the normed algebra of all bounded continuous scalar-valued mappings on X equipped with pointwise addition and multiplication and the supremum norm, we study its spectrum, denoted by 𝔰𝔭(H). We make a correspondence between algebraic properties of H and topological properties of 𝔰𝔭(H). This continues

Kaimakamis and Panagiotidou in [Taiwanese J. Math. 18(6) (2014), 1991–1998] proposed an open question: are there real hypersurfaces in nonflat complex space forms whose ∗-Ricci tensor satisfies the condition of 𝔻-parallelism? In this short note, we present an affirmative answer and prove that a three-dimensional real hypersurface in a nonflat complex space form has 𝔻-parallel ∗-Ricci tensor if and

In this paper, we prove a global well-posedness of the three-dimensional incompressible Navier-Stokes equation under initial data, which belongs to the Lei-Lin-Gevrey space Za,σ−1(ℝ3) and if the norm of the initial data in the Lei-Lin space 𝓧−1 is controlled by the viscosity. Moreover, we will show that the norm of this global solution in the Lei-Lin-Gevrey space decays to zero as time approaches

In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types induced aggregation operators, namely induced interval-valued Pythagorean fuzzy ordered weighted geometric aggregation operator, induced interval-valued Pythagorean fuzzy hybrid geometric

Let K be the restricted contact Lie algebras K(n, ) over an algebraically closed field F of characteristic p > 3. We prove that each skew-symmetric biderivation of K is inner and show that commuting maps on K are scalar multiplication maps. Moreover, it is showed that the commuting automorphisms and dertivations of K are proved to be the identity mappings and zero mappings, respectively. Meanwhile