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This paper studies the steady boundary layer flow over an impermeable moving vertical flat plate with convective boundary condition at the left side of the flat plate. The governing partial differential equations are transformed into a system of ordinary (similarity) differential equations by using corresponding similarity variables. These equations were then solved numerically using the function bvp4c from Matlab for different values of the Rayleigh number Ra, the convective heat transfer parameter $$\gamma $$ , and the Prandtl number Pr. This paper demonstrates that a similarity solution is possible if the convective boundary condition heat transfer is associated with the hot or cooled fluid on the left side of the flat plate proportional to $$x^{-1/4}$$ . For the sake of comparison of the numerical results, the case of the static flat plate $$(\sigma =0)$$ has been also studied. For the case of a moving flat plate $$(\sigma =1)$$ , it is shown that the solutions have two branches in a certain range of the positive (assisting flow) and negative (opposing flow) values of the Rayleigh number Ra. In order to test the physically available solutions, a stability analysis has been also performed. The effects of the governing parameters on the skin friction, heat transfer, wall temperature, velocity and temperature profiles, as well as on the streamlines and isotherms are investigated. Comparison with results from the open literature shows a very good agreement.

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z4-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

In this paper we study the partial hedging of American options in discrete time and complete markets. This problem leads to a stochastic game maximizing over stopping times and minimizing over stochastic processes satisfying a budget constraint. In the first part of the paper we introduce a dual problem maximizing over two-dimensional vectors of randomized stopping times and parametrized by Lagrange multipliers. We show that the value function of the hedging problem is conjugate to the dual problem. The solution to the dual problem for a fixed Lagrange multiplier is given as the solution of a two-dimensional coupled singular control problem under which the American option is decomposed in terms of risk and cost. In the second part of the paper we show, under a Markov assumption, the existence of an optimal deterministic Markov policy with respect to an enlarged state process.

In a Hilbert space setting ${\mathcal{H}}$, in order to minimize by fast methods a general convex lower semicontinuous and proper function ${\Phi }: {\mathcal{H}} \rightarrow \mathbb {R} \cup \{+\infty \}$, we analyze the convergence rate of the inertial proximal algorithms. These algorithms involve both extrapolation coefficients (including Nesterov acceleration method) and proximal coefficients in a general form. They can be interpreted as the discrete time version of inertial continuous gradient systems with general damping and time scale coefficients. Based on the proper setting of these parameters, we show the fast convergence of values and the convergence of iterates. In doing so, we provide an overview of this class of algorithms. Our study complements the previous Attouch–Cabot paper (SIOPT, 2018) by introducing into the algorithm time scaling aspects, and sheds new light on the Guler seminal papers on the convergence rate of the accelerated proximal methods for convex optimization.

Let $$(U(t))_ {t\ge 0}$$ be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) $$t>0$$ . In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space.

In this paper, we deal with the following singularly perturbed elliptic problem $$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}$$ where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as $${\varepsilon \rightarrow 0}$$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.

We introduce here the notion of conformal semi-Riemannian map between semi-Riemannian manifolds aiming to unify and generalize two geometric concepts. The first one is studied by Garcia-Rio and Kupeli (namely, semi-Riemannian map between semi-Riemannian manifolds). The second notion is defined by Aahin (namely, conformal Riemannian map between Riemannian manifolds) as an extension of the notion of Riemannian map introduced by Fischer. We support the main notion of this paper with several classes of examples, e.g. semi-Riemanninan submersions (see O'Neill's book and Falcitelli, Ianus and Pastore's book) and isometric immersions between semi-Riemannian manifolds. As a tool, we use the screen distributions (specific in semi-Riemannian geometry) of Duggal and Bejancu's book to obtain some characterizations and to give a semi-Riemannian version of Fischer's (resp. Aahin's) results, using the new map introduced here. We study the generalized eikonal equation and at the end relate the main notion of the paper with harmonicity.

This paper is devoted to introduce a numerical simulation with a theoretical study for flow of a Newtonian fluid over an impermeable stretching sheet which embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that proposed method is powerful mathematical tool and it can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

The present paper gives several subordination results involving a generalized Srivastava–Attiya operator (defined below). Among the results presented in this paper include also a sufficiency condition for the convexity of the convolution of certain functions and a sharp result relating to the convolution structure. We also mention various useful special cases of the main results including those which are related to the Zeta function.

This paper is a sequel to Choi (Math Ann 362(1–2):121–146, 2015) in Math. Ann. In that paper we studied the subharmonicity of Kahler–Einstein metrics on strongly pseudoconvex domains of dimension greater than or equal to 3. In this paper, we study the variations Kahler–Einstein metrics on bounded strongly pseudoconvex domains of dimension 2. In addition, we discuss the previous result with general bounded pseudoconvex domain and local triviality of a family of bounded strongly pseudoconvex domains.

In this paper, we introduce the normalized Shintani L-function of several variables by an integral representation and prove its functional equation. The Shintani L-function is a generalization to several variables of the Hurwitz-Lerch zeta function and the functional equation given in this paper is a generalization of the functional equation of Hurwitz-Lerch zeta function. In addition to the functional equation, we give special values of the normalized Shintani L-function at non-positive integers and some positive integers.

This paper deals with the existence and uniqueness of positive mild solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The existence and uniqueness of mild solution for the associated linear evolution equation nonlocal problem is established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness of positive mild solutions for nonlinear evolution equation nonlocal problem are obtained by using the monotone iterative method without the assumption of lower and upper solutions. The theorems proved in this paper improve and extend some related results in ordinary differential equations and partial differential equations. An example is also given to illustrate that our results are valuable.

The present paper is a survey aiming at characterizing all solutions of the discrete phase retrieval problem. Restricting ourselves to discrete signals with finite support, this problem can be stated as follows. We want to recover a complex-valued discrete signal $$\mathbf{x} :\mathbb {Z}\rightarrow \mathbb {C}$$ with support $$\{ 0, \ldots , N-1 \}$$ from the modulus of its discrete-time Fourier transform $$\widehat{x}(\omega )$$ . We will give a full classification of all trivial and nontrivial ambiguities of the discrete phase retrieval problem. In our classification, trivial ambiguities are caused either by signal shifts in space, by multiplication with a rotation factor $$\mathrm {e}^{\mathrm {i}\alpha }$$ , $$\alpha \in [-\pi , \pi )$$ , or by conjugation and reflection of the signal. Furthermore, we show that all nontrivial ambiguities of the finite discrete phase retrieval problem can be characterized by signal convolutions. In the second part of the paper, we examine the usually employed a priori conditions regarding their ability to reduce the number of ambiguities of the phase retrieval problem or even to ensure uniqueness. For the corresponding proofs we can employ our findings on the ambiguity classification. The considerations on the structure of ambiguities also show clearly the ill-posedness of the phase retrieval problem even in cases where uniqueness is theoretically shown.

We study the N = 1 super Schrodinger algebra S in (1 + 1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S.

It is well known that the Gaussian symplectic ensemble is defined on the space of \(n\times n\) quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices based on the exact known form of the density function of the eigenvalues (see Erdős in Russ Math Surv 66(3):507–626, 2011; Erdős in Probab Theory Relat Fields 154(1–2):341–407, 2012; Erdős et al. in Adv Math 229(3):1435–1515, 2012; Knowles and Yin in Probab Theory Relat Fields, 155(3–4):543–582, 2013; Tao and Vu in Acta Math 206(1):127–204, 2011; Tao and Vu in Electron J Probab 16(77):2104–2121, 2011). Due to the fact that multiplication of quaternions is not commutative, few works about large-dimensional quaternion self-dual Hermitian matrices are seen without normality assumptions. As in natural, we shall get more universal results by removing the Gaussian condition. For the first step, in this paper, we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to the semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.

In this paper we are concerned with the boundedness of Hormander–Mihlin multipliers of order $$\,r\, (1\le r1.$$ On the other hand the boundedness extends to $$\,\mathcal H_{2\pi }$$ if $$\,r>1,$$ but not if $$\,r=1.$$ Generalizing this result in the present paper we show that the scale of Hardy spaces $$\,\mathcal H^p_{2\pi }\, (01\,$$ we give a sharp bound $$\,p_rp_r\,$$ then the Hormander–Mihlin condition of order $$\,r\,$$ is sufficient on $$\mathcal H^p_{2\pi }$$ .

This paper analyses the image that one obtains by backprojecting synthetic aperture RADAR data collected on a flight-track with inflection points. The result is that one obtains artefacts that are of equal strength as the bona-fide part of the image. Furthermore, we obtain a weak normal form for operators associated to a fold/cusp canonical relation, which appears for our forward operator. Therefore this paper should be of use to researchers in different fields where such a structure arises.

This is an expository paper on Kahler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kahler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

The Hermite matrix polynomials have been generalized in a number of ways, and many of these generalizations have been shown to be important tools in applications. In this paper, we introduce a new generalization of the Hermite matrix polynomials and present the recurrence relations and the expansion of these new generalized Hermite matrix polynomials. We also give new series expansions of the matrix functions \(\exp (xB)\), \(\sin (xB)\), \(\cos (xB)\), \(\cosh (xB)\) and \(\sinh (xB)\) in terms of these generalized Hermite matrix polynomials and thus prove that many of the seemingly different generalizations of the Hermite matrix polynomials may be viewed as particular cases of the two-variable polynomials introduced here. The generalized Chebyshev and Legendre matrix polynomials have also been introduced in this paper in terms of these generalized Hermite matrix polynomials.

The purpose of this paper is to present a new iteration method based on the hybrid method in mathematical programming, extragradient method, and Mann’s method for finding a common element of the solution set of equilibrium problems, the solution set of variational inequality problems for a monotone, Lipschitz continuous mapping and the set of fixed points for a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence theorem for the sequences generated by this process. The results in this paper generalize and extend some well-known strong convergence theorems in the literature.

In this paper, we study a class of nonlinear Schrodinger–Poisson systems with indefinite steep potential well: $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\Delta u+V_{\lambda }(x)u+K(x)\phi u=|u|^{p-2}u &{} \text { in }\mathbb {R}^{3},\\ -\Delta \phi =K\left( x\right) u^{2} &{} \ \text {in }\mathbb {R}^{3}, \end{array} \right. \end{aligned}$$ where $$30$$ and $$ K(x)\ge 0$$ for all $$x\in \mathbb {R}^{3}$$ . We require that $$a\in C( \mathbb {R}^{3}) $$ is nonnegative and has a potential well $$\Omega _{a}$$ , namely $$a(x)\equiv 0$$ for $$x\in \Omega _{a}$$ and $$a(x)>0$$ for $$x\in \mathbb {R}^{3}\setminus \overline{\Omega _{a}}$$ . Unlike most other papers on this problem, we allow that $$b\in C(\mathbb {R}^{3}) $$ is unbounded below and sign-changing. By introducing some new hypotheses on the potentials and applying the method of penalized functions, we obtain the existence of nontrivial solutions for $$\lambda $$ sufficiently large. Furthermore, the concentration behavior of the nontrivial solution is also described as $$\lambda \rightarrow \infty $$ .

In this paper, for the mapping of a sphere into a compact orientable manifold S n → M , n ⩾ 1 , we solve the problem of determining whether it represents a nontrivial element in the homotopy group of the manifold π n ( M ) πn(M ). For this purpose, we consistently use the theory of iterated integrals developed by K.-T. Chen. It should be noted that the iterated integrals as repeated integration were previously meaningfully used by Lappo-Danilevsky to represent solutions of systems of linear differential equations and by Whitehead for the analytical description of the Hopf invariant for mappings f : S 2 n - 1 → S n , n ⩾ 2 . We give a brief description of Chen’s theory, representing Whitehead’s and Haefliger’s formulas for the Hopf invariant and generalized Hopf invariant. Examples of calculating these invariants using the technique of iterated integrals are given. Further, it is shown how one can detect any element of the fundamental group of a Riemann surface using iterated integrals of holomorphic forms. This required to prove that the intersection of the terms of the lower central series of the fundamental group of a Riemann surface is a unit group.

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming, the descent-like method and the Halpern’s iteration method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a countably infinite family of nonexpansive mappings in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.

In this paper, we present a new multi-step algorithm for approximating a common element of the solution set of Ky Fan inequality and the set of common fixed points of a finite family of strict pseudo-contractive mappings in a real Hilbert space. This algorithm is based on Korpelevich’s extragradient method and viscosity approximation method. We prove a strong convergence theorem for the sequences generated by the algorithm. As applications, at the end of paper we utilize our results to study finding a common point of the solution set of an variational inequality problem and the fixed-point set of a finite family of strictly pseudo-contractive mappings. The results presented in this paper improve, extend, supplement and develop the corresponding results announced in the earlier and very recent literature.

In the paper [20], we gave a conjectural formula for the mixed Hodge polynomials of character varieties with generic semisimple conjugacy classes at punctures and we prove a formula for the \(E\)-polynomial. We also proved that these character varieties are irreducible [21]. In this paper, we extend the results of [20, 21] to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology. We also study Weyl group action on the intersection cohomology of the partial resolutions of these character varieties and give a conjectural formula for the two-variable polynomials that encode the trace of the elements of the Weyl group on the subquotients of the weight filtration. Finally, we compute the generating function of the stack count of character varieties with Zariski closure of unipotent regular conjugacy class at punctures.

In this paper, we consider a sequence of orbifold Kahler–Einstein metrics \((\omega _{X_m})_m\) and normalized Kahler–Ricci flows \((\omega _{X_m}(t))_m\) on a quasi-projective manifold \(X=\overline{X} {\setminus } \overline{D}\) for a projective manifold \(\overline{X}\) and a divisor \(\overline{D}\) of \(\overline{X}\) with simple normal crossings such that \(K_{\overline{X}}+\overline{D}\) is ample. For sufficiently large \(m, \omega _{X_m}\) or \(\omega _{X_m}(t)\) is the orbifold Kahler–Einstein metric or orbifold normalized Kahler–Ricci flow on \(X\) equipped with the orbifold structure with respect to the divisor \(1/m\overline{D}\), respectively. The main theorem of this paper is that the limit on the boundary \(\overline{D}\) or the inside \(X\) of the sequence \((\omega _{X_m}(t))_m\) as \(m \rightarrow \infty \) is exactly the complete normalized Kahler–Ricci flow on \(\overline{D}\) or \(X\), respectively. Moreover our method of the proof also leads to a result that on the boundary \(\overline{D}\) the sequence \((\omega _{X_m})_m\) converges to the complete Kahler–Einstein metric on \(\overline{D}\) as \(m \rightarrow \infty \).

In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.

In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials. The pseudo-resolvent approach is used., 10 pages, extended contribution to ISSPSM2005

This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane that imply the boundedness of the singular integral operator as well as the boundary behavior of the Cauchy type integral. These results are of significance for boundary value problems in domains with non-smooth and non-rectifiable boundaries.

In this paper, we introduce some new iteration methods combining the hybrid method in mathematical programming with Mann’s iterative method and the Halpern method for finding a fixed point of an asymptotically nonexpansive mapping and a common fixed point of an asymptotically nonexpansive semigroup in a Hilbert space. The main results in this paper modify and improve some well-known results in the literature.

Let $$\mathfrak {g}$$ be a symmetrizable Kac-Moody Lie algebra with the standard Cartan subalgebra $$\mathfrak {h}$$ and the Weyl group $$W$$ . Let $$P_+$$ be the set of dominant integral weights. For $$\lambda \in P_+$$ , let $$L(\lambda )$$ be the integrable, highest weight (irreducible) representation of $$\mathfrak {g}$$ with highest weight $$\lambda $$ . For a positive integer $$s$$ , define the saturated tensor semigroup as $$\begin{aligned} \Gamma _s:= \{(\lambda _1, \dots , \lambda _s,\mu )\in P_+^{s+1}: \exists \, N\ge 1 \,\text {with}\,L(N\mu )\subset L(N\lambda _1)\otimes \dots \otimes L(N\lambda _s)\}. \end{aligned}$$ The aim of this paper is to begin a systematic study of $$\Gamma _s$$ in the infinite dimensional symmetrizable Kac-Moody case. In this paper, we produce a set of necessary inequalities satisfied by $$\Gamma _s$$ . These inequalities are indexed by products in $$H^*(G^{\mathrm{min }}/B; \mathbb {Z})$$ for $$B$$ the standard Borel subgroup, where $$G^{\mathrm{min }}$$ is the ‘minimal’ Kac-Moody group with Lie algebra $$\mathfrak {g}$$ . The proof relies on the Kac-Moody analogue of the Borel-Weil theorem and Geometric Invariant Theory (specifically the Hilbert-Mumford index). In the case that $$\mathfrak {g}$$ is affine of rank 2, we show that these inequalities are necessary and sufficient. We further prove that any integer $$d>0$$ is a saturation factor for $$A^{(1)}_1$$ and 4 is a saturation factor for $$A^{(2)}_2$$ .

In this paper we continue the studies of the persistent effect of attraction of Newton-type iterations for optimality systems to critical Lagrange multipliers. It appears very important to understand the nature of this striking phenomenon, in particular, because it is precisely the reason of slow convergence of such methods when applied to problems with degenerate constraints. All previously known results concerned with this effect were a posteriori by nature: they were showing that in case of convergence, the dual limit is in a sense unlikely to be noncritical. This paper suggests the first a priori result in this direction, showing that critical multipliers actually serve as attractors: for a fully quadratic optimization problem with equality constraints, under certain reasonable assumptions we establish actual local convergence of the Newton---Lagrange method to a critical multiplier starting from a "dense" set around a given critical multiplier. This is an important step forward in understanding the attraction phenomenon.

In the present paper, we study the nature of LP-Sasakian manifolds admitting the M-projective curvature tensor. It is examined whether this manifold satisfies the condition W(X, Y ).R = 0. Moreover, it is proved that, in the M-projectively flat LP-Sasakian manifolds, the conditions R(X, Y ).R = 0 and R(X, Y ).S = 0 are satisfied. In the last part of the paper, an M-projectively flat space-time is introduced, and some properties of this space are obtained.

In an earlier paper Buczolich, Elekes and the author introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. They proved that it is precisely the right notion to describe the Hausdorff dimension of the level sets of the generic real-valued continuous function (in the sense of Baire category) defined on a compact metric space \(K\). The goal of this paper is to determine the Hausdorff dimension of the fibers of the generic continuous function from \(K\) to \(\mathbb {R}^n\). In order to do so, we define the \(n\)th inductive topological Hausdorff dimension, \(\dim _{t^nH} K\). Let \(\dim _H K,\,\dim _t K\) and \(C_n(K)\) denote the Hausdorff and topological dimension of \(K\) and the Banach space of the continuous functions from \(K\) to \(\mathbb {R}^n\). We show that \(\sup _{y\in \mathbb {R}^n} \dim _{H}f^{-1}(y) = \dim _{t^nH} K -n\) for the generic \(f \in C_n(K)\), provided that \(\dim _t K\ge n\), otherwise every fiber is finite. In order to prove the above theorem we give some equivalent definitions for the inductive topological Hausdorff dimensions, which can be interesting in their own right. Here we use techniques coming from the theory of topological dimension. We show that the supremum is actually attained on the left hand side of the above equation. We characterize those compact metric spaces \(K\) for which \(\dim _{H} f^{-1}(y)=\dim _{t^nH}K-n\) for the generic \(f\in C_n(K)\) and the generic \(y\in f(K)\). We also generalize a result of Kirchheim by showing that if \(K\) is self-similar and \(\dim _t K\ge n\) then \(\dim _{H} f^{-1}(y)=\dim _{t^nH}K-n\) for the generic \(f\in C_n(K)\) for every \(y\in {{\mathrm{int}}}f(K)\).

In this paper, the authors consider a family of smooth immersions Ft: Mn → Nn+1 of closed hypersurfaces in Riemannian manifold Nn+1 with bounded geometry, moving by the Hk mean curvature flow. The authors show that if the second fundamental form stays bounded from below, then the Hk mean curvature flow solution with finite total mean curvature on a finite time interval [0, Tmax) can be extended over Tmax. This result generalizes the extension theorems in the paper of Li (see “On an extension of the Hk mean curvature flow, Sci. China Math., 55, 2012, 99–118”).

This paper is concerned with the existence of \(\alpha \)-mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space. We assume that the linear part generates a compact, analytic and uniformly bounded semigroup, the nonlinear part satisfies some local growth conditions in Hilbert space \(\mathbb {H}\) and the nonlocal term satisfies some local growth conditions in fractional power space \(\mathbb {H}_\alpha \). The result obtained in this paper improves and extends some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract result.

In this paper we consider a sum of modified Bessel functions of the first kind of which particular case is used in the study of Kanter's sharp modified Bessel function bound for concentrations of some sums of independent symmetric random vectors. We present some monotonicity and convexity properties for that sum of modified Bessel functions of the first kind, as well as some Tur\'an type inequalities, lower and upper bounds. Moreover, we point out an error in Kanter's paper [Ka] and at the end of the paper we pose an open problem, which may be of interest for further research., Comment: 8 pages

In our former paper (Noguchi et al. in J. Math. Pures Appl. 88:293–306, 2007) we proved an algebraic degeneracy of entire holomorphic curves into a variety X which carries a finite morphism to a semi-abelian variety, but which is not isomorphic to a semi-abelian variety by itself. The finiteness condition of the morphism is necessary in general by example. In this paper we improve that finiteness condition under an assumption such that some open subset of non-singular points of X is of log-general type, and simplify the proof in (Noguchi et al. in J. Math. Pures Appl. 88:293–306, 2007), which was rather involved. As a corollary it implies that every entire holomorphic curve $f:\mathbb{C} \to V$ into an algebraic variety V with $\bar{q}(V)\geq\dim V=\bar {\kappa}(V)$ is algebraically degenerate, which is due to Winkelmann (dimV=2) (Winkelmann in Ann. Inst. Fourier 61:1517–1537, 2011) and Lu–Winkelmann (Lu and Winkelmann in Forum Math. 24:399–418, 2012).

The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of points satisfying the Equilibrium problem, variational inequality and fixed point problems of a strict pseudocontraction mapping in Hilbert spaces. Consequently, we obtain the strong convergence of an iterative algorithm generated by the hybrid extragradient projection method. The results presented in this paper generalize, improve and extend some well-known results in the literature.

In this paper, explicit determination of the cyclotomic numbers of order l and 2 l , for odd prime l ≡ 3 (mod 4), over finite field F q in the index 2 case are obtained, utilizing the explicit formulas on the corresponding Gauss sums. The main results in this paper are related with the number of rational points of certain elliptic curve, called "Legendre curve", and the properties and value distribution of such number are also presented.

In this paper, we consider the following equation u t = ( u m ) xx + ( u n ) x , with the initial condition as Dirac measure. Attention is focused on existence, nonexistence, uniqueness and the asymptotic behavior near (0, 0) of solution to the Cauchy's problem. The special feature of this equation lies in nonlinear convection effect, i.e., the equation possesses nonlinear hyperbolic character as well as degenerate parabolic one. The situation leads to a more sophisticated mathematical analysis. To our knowledge, the solvability of singular solution to the equation has not been concluded yet. Here based on the previous works by the authors, we show that there exists a critical number n 0 = m +2 such that a unique source-type solution to this equation exists if 0 ≤ n n 0 , while such a solution does not exist if n ≥ n 0 (see our working paper). Our results give the perfect answer to such topical researches.

This paper mainly considers the coupled parabolic system in a bounded domain: ut = Δu + uαvp, vt = Δv + uqvβ in Ω × (0, T) with null Dirichlet boundary value condition which had been discussed by Wang in (Z Angew Math Phys 51:160–167, 2000). The aim of this paper is to solve the open problem mentioned in the Remark of Wang (Z Angew Math Phys 51:160–167, 2000).

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell’s equations. Precisely, for the case with a perfectly electric conducting (PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete H 1-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L 2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell’s equations introduced in this paper. Furthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.

The paper is devoted to spectral problems for strongly elliptic second-order systems in bounded Lipschitz domains. We consider the spectral Dirichlet and Neumann problems and three problems with spectral parameter in conditions at the boundary: the Poincare–Steklov problem and two transmission problems. In the style of a survey, we discuss the main properties of these problems, both self-adjoint and non-self-adjoint. As a preliminary, we explain several facts of the general theory of the main boundary value problems in Lipschitz domains. The original definitions are variational. The use of the boundary potentials is based on results on the unique solvability of the Dirichlet and Neumann problems. In the main part of the paper, we use the simplest Hilbert L2-spaces Hs, but we describe some generalizations to Banach spaces Hsp of Bessel potentials and Besov spaces Bsp at the end of the paper.

It is well known that the validity of the so called Lenard–Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalgebra or Lie conformal superalgebra. The most relevant are certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology complexes, which we identify (non-canonically) with the generalized de Rham complex and the generalized variational complex. In the second part of the paper we compute the cohomology of the generalized de Rham complex, and, via a detailed study of the long exact sequence, we compute the cohomology of the generalized variational complex for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient. For the latter we use some differential linear algebra developed in the Appendix., National Science Foundation (U.S.), ERC (Advanced Grant)

This paper studies the Fermat point in Hilbert spaces for a system of n distinct points. We prove the existence of the Fermat point and we determine its location in the convex hull of the given system of points. A new concept of Fermat point for a non–discrete set of points is introduced and there are proved similar results to discrete case. In the second part of this paper we give close form formulas of Fermat point for a system of 3 and 4 distinct points. We also describe some iterative methods to find the Fermat point for a system of more than 4 distinct points.

In a recent paper, El-Shahed and Gaber (Appl Math Comput 217, pp 9165–9172, 2011) have introduced and studied the two-dimensional q-differential transform method. We observe that, in their work some results giving the q-differential transform of product of two functions are erroneous. In the present paper, we first provide their corrected forms as Theorem 1 and Corollary 1. We then apply this method to solve two q-differential equations.

This paper is devoted to planar stationary line segment processes. The segments are assumed to be independent, identically distributed, and independent of the locations (reference points). We consider a point process formed by self-crossing points between the line segments. Its asymptotic variance is explicitly expressed for Poisson segment processes. The main result of the paper is the central limit theorem for the number of intersection points in expanding rectangular sampling window. It holds not only for Poisson processes of reference points but also for stationary point processes satisfying certain conditions on absolute regularity (β-mixing) coefficients. The proof is based on the central limit theorem for β-mixing random fields. Approximate confidence intervals for the intensity of intersections can be constructed.

This paper is a continuation of our work in Grobbelaar-Van Dalsen (Appl Anal 90:1419–1449, 2011) where we showed the strong stability of models involving the thermoelastic Mindlin–Timoshenko plate equations with second sound. For the case of a plate configuration consisting of a single plate, this was accomplished in radially symmetric domains without applying any mechanical damping mechanism. Further to this result, we establish in this paper the non-exponential stability of the model for a particular configuration under mixed boundary conditions on the shear angle variables and Dirichlet boundary conditions on the displacement and thermal variables when the heat flux is described by Fourier’s law of heat conduction. We also determine the rate of polynomial decay of weak solutions of the model in a radially symmetric region under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables.

Umeda et al. (Jpn J Appl Math 1:435–457, 1984) considered a rather general class of symmetric hyperbolic–parabolic systems: $$A^{0}z_{t}+\sum_{j=1}^{n}A^{j}z_{x_{j}}+Lz=\sum_{j,k=1}^{n}B^{jk}z_{x_{j}x_{k}}$$ and showed optimal decay rates with certain dissipative assumptions. In their results, the dissipation matrices $${L}$$ and $${B^{jk}(j,k=1,\ldots,n)}$$ are both assumed to be real symmetric. So far there are no general results in case that $${L}$$ and $${B^{jk}}$$ are not necessarily symmetric, which is left open now. In this paper, we investigate compressible Navier–Stokes–Maxwell (N–S–M) equations arising in plasmas physics, which is a concrete example of hyperbolic–parabolic composite systems with non-symmetric dissipation. It is observed that the Cauchy problem for N–S–M equations admits the dissipative mechanism of regularity-loss type. Consequently, extra higher regularity is usually needed to obtain the optimal decay rate of $${L^{1}({\mathbb{R}}^3)}$$ - $${L^2({\mathbb{R}}^3)}$$ type, in comparison with that for the global-in-time existence of smooth solutions. In this paper, we obtain the minimal decay regularity of global smooth solutions to N–S–M equations, with aid of $${L^p({\mathbb{R}}^n)}$$ - $${L^{q}({\mathbb{R}}^n)}$$ - $${L^{r}({\mathbb{R}}^n)}$$ estimates. It is worth noting that the relation between decay derivative orders and the regularity index of initial data is firstly found in the optimal decay estimates.