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In this paper, we obtain the existence of at least two standing waves (and homoclinic solutions) for a class of time-dependent (and time-independent) discrete nonlinear Schrödinger systems or equations. The novelties of the paper are as follows. (1) Our nonlinearities are composed of three mixed growth terms, i.e., the nonlinearities are composed of sub-linear, asymptotically-linear and super-linear terms. (2) Our nonlinearities may be sign-changing. (3) Our results can also be applied to the cases of concave-convex nonlinear terms. (4) Our results can be applied to a wide range of mathematical models. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method. [ABSTRACT FROM AUTHOR]

In this paper, we provide some algebraic structures of convex subrings of *C, a nonstandard extension of the field of complex numbers C. In particular, a detailed description of the prime spectrum of any convex subring of *C is given. To achieve our goal, first we investigate prime ideals and we characterize two consecutive elements in the spectrum of a divided domain. We also show that the prime spectrum of the ring of bounded hypercomplex numbers has two peculiar properties: there are no three consecutive elements in the spectrum; moreover, nonzero elements are a disjoint union of three subsets where one of them is strongly dense and the other two are dense in the spectrum. [ABSTRACT FROM AUTHOR]

The paper is concerned with Jacobi matrices having periodic or asymptotically periodic coefficients. In the first part, we give an elementary derivation of the well-known density of states of Jacobi matrices with periodic coefficients; our approach is independent from the standard arguments using Floquet theory or potential theory. In the last part of the paper, we extend the results of Van Assche, published in 1999, on Jacobi matrices with asymptotically periodic coefficients depending on a parameter. [ABSTRACT FROM AUTHOR]

Denote by G the group of interval exchange transformations (IETs) on the unit interval. Let Gper ⊂ G be the subgroup generated by torsion elements in G (periodic IETs) and let Grot ⊂ G be the subset of 2-IETs (rotations). The elements of the subgroup H = Gper,Grot ⊂ G (generated by the sets Gper and Grot) are characterized constructively in terms of their Sah-Arnoux- Fathi (SAF) invariant. The characterization implies that a non-rotation type 3-IET lies in H if and only if the lengths of its exchanged intervals are linearly dependent over Q. In particular, H ⊄G. The main tools used in the paper are the SAF invariant and a recent result by Y. Vorobets that Gper coincides with the commutator subgroup of G. [ABSTRACT FROM AUTHOR]

This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give a characterization for polynomials and rational functions which admit only non-negative values on definable sets in real closed valued fields. That is, generalizing the relative Positivstellensatz for sets defined also by valuation terms. For this, we use model theoretic tools, together with existence of canonical valuations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that is, the solution converges to a positive constant), we use phase plane analysis and upper/lower solutions to prove that the rightward and leftward asymptotic spreading speeds exist and both are positive constants. Moreover, one of them is bigger and the other is smaller than the spreading speed in the corresponding problem without advection term. [ABSTRACT FROM AUTHOR]

Let n ≥ 3 be an integer, and let Σn be a non-totally geodesic complete minimal hypersurface immersed in the (n + 1)-dimensional space form M̅n+1 (c), where the constant c denotes the sectional curvature of the space form. If Σn satisfies the Simons’ equation (3.9), then either (1) Σn is a catenoid if c ≤ 0, or (2) Σn is a Clifford minimal hypersurface or a compact Ostuki minimal hypersurface if c > 0. This paper is motivated by a 2009 work of Tam and Zhou. [ABSTRACT FROM AUTHOR]

We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the N-dimensional case. In the second part of the paper, our method is adapted to handle the axisymmetric incompressible Euler equations with swirl. [ABSTRACT FROM AUTHOR]

In the present paper we obtain several new results related to the problem of upper bound estimates for the number of solutions of the congruence.....where p is a large prime number and λ is an integer coprime to p. Our arguments are based on recent estimates of trigonometric sums over subgroups due to Shkredov and Shteinikov. [ABSTRACT FROM AUTHOR]

This paper is concerned with a diffusive logistic model in population ecology. As observed by Y. Lou, in a spatially heterogeneous environment, this model can always support a total population at equilibrium greater than the total carrying capacity. In other words, the ratio of the total population at equilibrium to the total carrying capacity is always larger than 1. Our goal is to find the supremum of this ratio taken over all possible choices of spatial distributions of resources and the species' dispersal rate. A conjecture proposed by W.-M. Ni is that, in the one-dimensional case, the supremum is 3. We settle this conjecture and then apply our result to study the global dynamics of a heterogeneous Lotka-Volterra competition-diffusion system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate continuity and integrability properties of the second order derivatives of viscosity solutions of a certain uniformly elliptic Isaacs equation. We give sufficient and necessary conditions for continuity of the second order derivatives and give sufficient conditions for interior W2,p regularity, 1 < p < ∝. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and alsofor the level set mean curvature flow, which is an example of singular degenerate equations. We prove that the modulus of continuity is a viscosity subsolution of some one-dimensional equation. This work extends B. Andrews' recent result on moduli of continuity for smooth spatially periodic solutions. [ABSTRACT FROM AUTHOR]

The paper presents a Fock space model suitable for construction of c-free algebras. Immediate applications are direct proofs for the properties of the c-free R- and S-transforms. [ABSTRACT FROM AUTHOR]

In this paper we consider the sequences of polynomials {Q(α)n }n≥0, orthogonal with respect to the inner product ≺f, g≻v = ⌠+∞0 f(x)g(x)dμ(x) + mΣ j=1 aj f(cj)g(cj ), where dμ(x) = xαe-x is the Laguerre measure on R...+, α>-1, cj < 0, aj > 0 and f, g are polynomials with real coefficients. We first focus our attention on the representation of these polynomials in terms of the standard Laguerre polynomials. Next we find the explicit formula for their outer relative asymptotics, as well as the holonomic equation that such polynomials satisfy. Finally, an electrostatic interpretation of their zeros in terms of a logarithmic potential is presented. [ABSTRACT FROM AUTHOR]

In this paper, we link the nature of special values of certain Dirichlet L-functions to those of multiple gamma values. [ABSTRACT FROM AUTHOR]

The result stated in the title is proved, thereby disproving the result shown in a 1983 paper by B. A. Barnes (Theorem 4.1). [ABSTRACT FROM AUTHOR]

In this paper, we prove via counterexamples that adding an advection term of the form Shear flow (whose streamlines are parallel to the direction of propagation) to a reaction-diffusion equation will be enough heterogeneity to spoil the increasing behavior of the KPP speed of propagation with respect to diffusion. The non-monotonicity of the speed with respect to diffusion will occur even when the reaction term and the diffusion matrices are considered homogeneous (do not depend on space variables). For the sake of completeness, we announce our results in a setting which allows domains with periodic perforations that may or may not be equal to the whole space ℝN. [ABSTRACT FROM AUTHOR]

In this paper we develop formulae for inverting the so-called cosh-weighted Hilbert transform Hμ, which arises in Single Photon Emission Computed Tomography (SPECT). The formulae are theoretically exact, require a minimal amount of data, and are similar to the classical inversion formulae for the finite Hilbert transform (FHT) H0. We also find the null-space and the range of Hμ in Lp with p > 1. Similarly to the FHT, the null-space turns out to be one-dimensional in Lp for any p ∈ (1,2) and trivial - for p ≥ 2. We prove that Hμ is a Fredholm operator of index - 1 when it acts between the Lp spaces, p ∈ (1,∞, p/ 2. Finally, in the case where p ≠ 2 we find the range condition for Hμ, which is similar to that for the FHT H0. Our work is based on the method of the Riemann-Hilbert problem. [ABSTRACT FROM AUTHOR]

In this paper we give a sufficient condition on the class numbers of distinct quadratic imaginary fields so that on a given CM elliptic curve over Q with fixed modular parameterization, the Heegner points associated to (the maximal orders of) these quadratic imaginary fields are linearly independent. This extends results of Rosen and Silverman from the non-CM to the CM case. [ABSTRACT FROM AUTHOR]

This paper concerns harmonic measure on the domains that arise when infinitely many disjoint closed discs are removed from the unit disc. It investigates which configurations of discs are unavoidable for Brownian motion and obtains refinements of related results of Akeroyd, and of Ortega-Cerd`a and Seip. [ABSTRACT FROM AUTHOR]

This paper gives a proof for the existence and nonexistence of traveling wave solutions of a reaction-convection epidemic model for the spatial spread of H5N1 avian influenza involving a wide range of bird species and environmental contamination. The threshold condition for the existence of traveling waves coincides with the basic reproduction number exceeding one. The existence of wave solutions is obtained by constructing an invariant cone of initial functions defined on a large spatial domain, applying a fixed point theorem on this cone and then a limiting argument. The invariant cone is based on the information of initial growth pattern of the epidemic and the final size estimation during the entire course of the outbreak. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show that the recent proof by Ganyushkin, Mazorchuk and Steinberg of the parametrisation of simple modules over finite semigroup algebras due to Clifford, Munn and Ponizovski?i carries over to twisted finite category algebras. We observe that the parametrisations of simple modules over Brauer algebras, Temperley-Lieb algebras, and Jones algebras due to Graham and Lehrer can be obtained as special cases of our main result. We further note that the notion of weights in the context of Alperin's weight conjecture extends to twisted finite category algebras. [ABSTRACT FROM AUTHOR]

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, ut = uxx + λu - β(t)u3, and investigate the bifurcations that this attractor undergoes as λ is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case. [ABSTRACT FROM AUTHOR]

Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with uniform control of the norm in the Hardy space of bounded analytic functions on the disk, then the sequence is an interpolating sequence (i.e. every bounded sequence of values can be interpolated by functions in the Hardy space). It turns out that such a result holds in other spaces. In this short paper we would like to show that for a given sequence it is sufficient to find just one function suitably interpolating zeros as well as ones to deduce interpolation in the Hardy space. The result has an interesting interpretation in the context of model spaces. [ABSTRACT FROM AUTHOR]

We study a class of stochastic Bernstein polynomials built from order statistics of identically, independently, and uniformly distributed random variables on [0, 1]. We establish a Chebyshev type inequality for the probabilistic convergence of a stochastic Bernstein polynomial sequence to its target function. This is a major improvement of the main result of Wu, Sun, and Ma [Adv. Comput. Math. 38 (2013), no. 1, pp. 187-205]. Moreover, the method we develop here in dealing with varying-weighted sums of dependent random variables is of independent interest. [ABSTRACT FROM AUTHOR]

On page 43 in [Adv. in Math. 50 (1983), pp. 27-48] Sorin Popa asked whether the following property holds: If ω is a free ultrafilter on N and R1 ⊆ R is an irreducible inclusion of hyperfinite II1 factors such that R' ∩ Rω ⊆ Rω1 does it follows that R1 = R? In this short note we provide an affirmative answer to this question. [ABSTRACT FROM AUTHOR]

We present a previously unpublished proof of the conservativity of WKL0 over IΣ1 using the Arithmetized Completeness Theorem, which, in particular, constitutes an ω-interpretation of WKL0 in IΣ1. We also show that WKL0* is interpretable in IΔ0 + exp. [ABSTRACT FROM AUTHOR]

In this paper, a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response is studied. By using the continuation theorem of coincidence degree theory, easily verifiable criteria are established for the existence of positive periodic solutions to the system. [ABSTRACT FROM AUTHOR]

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction $ -u^p$ and set in $ \mathbb{R}^N$ that behaves like a negative power at infinity. That is, $ \vert x\vert^\alpha u_0(x)\to A>0$ $ \vert x\vert\to\infty$ $ 0<\alpha\le N$1+2/\alpha$ --> $ p>1+2/\alpha$ $ \mathfrak{a}$ [ABSTRACT FROM AUTHOR]

Let $(X,ast )$ be a pointed CW-complex, $K$ be a simplicial complex on $n$ vertices and $X^K$ be the associated polyhedral power. In this paper, we construct a Sullivan model of $X^K$ from $K$ and from a model of $X$. par Let $mathcal {F}(K,X)$ be the homotopy fiber of the inclusion $X^Kto X^n$. Recent results of Grbic and Theriault, on one side, and of Denham and Suciu, on the other side, show the diversity of the possible homotopy types for $mathcal {F}(K,X)$. Here, we prove that the corresponding map between Sullivan models is Golod attached, generalizing a result of J. Backelin. This property is deduced from the existence of a succession of fibrations whose fibers are suspensions. par We consider also the Lusternik-Schnirelmann category of $X^K$. In the case that $operatorname {cat}X^n=noperatorname {cat}X$, we prove that $operatorname {cat}X^K =(operatorname {cat}X)(1+dim K)$. par Finally, we mention that this work is written in the case of a sequence of pairs, $underline {X}=(X_i,A_i)_{1leq ileq n}$, as in a recent work of Bahri, Bendersky, Cohen and Gitler. [ABSTRACT FROM AUTHOR]

We provide a pointwise bipolar theorem for lim inf-closed convex sets of positive Borel measurable functions on a σ-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a version of the transport duality under nontight marginals, and a superhedging duality for semistatic hedging in discrete time. [ABSTRACT FROM AUTHOR]

We describe the distribution of the number and location of the fixed points of permutations that avoid the pattern 321 via a bijection with rooted ordered trees on n+1 vertices. Using the local limit theorem for Galton- Watson trees, we are able to give an explicit description of the limit of this distribution. [ABSTRACT FROM AUTHOR]

The Carlson-Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, there is an infinite sequence with infinitely many variables such that for every valuation, some specific set of initial segments is homogeneous. Friedman, Simpson, and Montalban asked about its reverse mathematical strength. We study the computability-theoretic properties and the reverse mathematics of this statement, and relate it to the finite union theorem. In particular, we prove the Ordered Variable word for binary strings in ACA0. [ABSTRACT FROM AUTHOR]

A classical result of J.-L. Lions asserts that if a solution to the Navier-Stokes equations is such that (i) it is in the Leray-Hopf class and (ii) belongs to L4(0, T;L4), then it must satisfy the energy equality in the time interval [0, T]. In this note we show that assumption (i) is not necessary. [ABSTRACT FROM AUTHOR]

Let R be a local ring of dimension d. Buchweitz asks if the rank of the dth syzygy of a module of finite lengh is greater than or equal to the rank of the dth syzygy of the residue field, unless the module has finite projective dimension. Assuming that R is Gorenstein, we prove that if the answer is affirmative, then R is a hypersurface. If moreover R has dimension two, then we show that the converse also holds true. [ABSTRACT FROM AUTHOR]

A measurable function µ on the unit disk D of the complex plane with ∥µ∥8 < 1 is sometimes called a Beltrami coefficient. We say that µ is trivial if it is the complex dilatation f¯z/fz of a quasiconformal automorphism f of D satisfying the trivial boundary condition f(z) = z, |z| = 1. Since it is not easy to solve the Beltrami equation explicitly, to detect triviality of a given Beltrami coefficient is a hard problem, in general. In the present article, we offer a sufficient condition for a Beltrami coefficient to be trivial. Our proof is based on Betker's theorem on Lowner chains. [ABSTRACT FROM AUTHOR]

We show that the height density of a finite sum of fractions is zero. In fact, we give quantitative estimates in terms of the height function. Then, we focus on the unit fraction solutions in the ring of integers of a given number field. In particular, we prove that finitely many representations of 1 as a sum of unit fractions determines the field of rational numbers among all real number fields. Finally, using non-standard methods, we prove some density and finiteness results on a finite sum of fractions. [ABSTRACT FROM AUTHOR]

In this note we study the regularity properties of the discrete maximal operators at endpoint. Precisely, we show that the general discrete centered and non-centered maximal operators are bounded and continuous from l¹(Z) to BV(Z), as well as the non-centered discrete maximal operator maps BV(Z) → BV(Z) boundedly under a more restrictive condition, where BV(Z) denotes the set of functions of bounded variation defined on Z. As an immediate consequence, we obtain somewhat unexpected endpoint regularities of the discrete fractional maximal functions. [ABSTRACT FROM AUTHOR]

Using some formulas of hypergeometric series and properties of the gamma function, we deduce certain p-adic supercongruence relations concerning truncated hypergeometric series. As consequences, we confirm the conjectural supercongruences (see Conjecture 1.2 [Proc. Amer. Math. Soc. 145 (2017), no. 2, 501-508]) posed by Bing He and extend them to all primes. [ABSTRACT FROM AUTHOR]

In this note we prove a result on the multiplicative independence of the numbers m - α, n - α, where m > n are positive integers and α is a reciprocal algebraic number with the property that α+1/α has at least two real conjugates over ℚ lying in the interval (-∞, 2]. As an application, we show that for any positive integers m > n and k ⩾ 3 the numbers m - ζk, n - ζk, where ζk is the primitive kth root of unity, are multiplicatively independent except when (n, k) = (1, 6). This settles a recent conjecture of Madritsch and Ziegler. [ABSTRACT FROM AUTHOR]

We define a one-parametric family of positions of a centrally symmetric convex body K which interpolates between the John position and the Loewner position: for r > 0, we say that K is in maximal intersection position of radius r if Voln(K n rBn2) = Voln(K n rTBn2) for all T ∊ SLn. We show that under mild conditions on K, each such position induces a corresponding isotropic measure on the sphere, which is simply the normalized Lebesgue measure on r-1K n Sn-1. In particular, for rM satisfying rnM κn = Voln(K), the maximal intersection position of radius rM is an M-position, so we get an M-position with an associated isotropic measure. Lastly, we give an interpretation of John's theorem on contact points as a limit case of the measures induced from the maximal intersection positions. [ABSTRACT FROM AUTHOR]

We deduce a formula for the exact number of gridpoints (i.e., elements of Zd) in the extended d-dimensional cube nCd = [-n,+n]d on intersecting hyperplanes. In the special case of the hyperplanes {x ∈ Rd | x1 +· · ·+xd = b}, b ∈ Z, these numbers can be written as a finite sum involving products of certain binomial coefficients. Furthermore, we consider the limit as n tends to infinity which can be expressed in terms of Euler-Frobenius numbers. Finally, we state a conjecture on the asymptotic behaviour of this limit as the dimension d tends to infinity. [ABSTRACT FROM AUTHOR]

Given a nontrivial family of pairs of faces of unital C*-algebras where each pair has a faithful state, it is proved that if the bifree product state is faithful on the reduced bifree product of this family of pairs of faces, then each pair of faces arises as a minimal tensor product. A partial converse is also obtained. [ABSTRACT FROM AUTHOR]

Let E(n)kk denote the minimax (i.e., best supremum norm) error in approximation of xn on [0, 1] by rational functions of type (k, k) with k < n. We show that in an appropriate limit E(n)kk ~ 2Hk+1/2 independently of n, where H ≈ 1/9.28903 is Halphen's constant. This is the same formula as for minimax approximation of ex on (-∞, 0]. [ABSTRACT FROM AUTHOR]

A generating function for the Bannai-Ito polynomials is derived using the fact that these polynomials are known to be essentially the Racah or 6j coefficients of the osp(1|2) Lie superalgebra. The derivation is carried in a realization of the recoupling problem in terms of three Dunkl oscillators. [ABSTRACT FROM AUTHOR]

Let Fp be a prime field of order p > 2, and let A be a set in Fp with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A × A satisfies |(A - A)³ + (A - A)³| ≫ |A|8/7, which improves a result due to Yazici, Murphy, Rudnev, and Shkredov. In addition, we investigate some new families of expanders in four and five variables. We also give an explicit exponent of a problem of Bukh and Tsimerman, namely, we prove that max {|A + A|, |f(A,A)|} ≫ |A|6/5, where f(x, y) is a quadratic polynomial in Fp[x, y] that is not of the form g(αx + βy) for some univariate polynomial g. [ABSTRACT FROM AUTHOR]

We show that characteristic functions of domains with piecewise C³ boundaries transversal to suitable cones are bounded multipliers on a recently introduced scale UpC,t,s of anisotropic Banach spaces, under the conditions -1 + 1/p < s < -t < 0, with p ∈ (1, ∞). [ABSTRACT FROM AUTHOR]

In this note, we employ the techniques of Malliavin calculus to provide some sufficient conditions for a stochastic process to satisfy Novikov's criterion. In particular, we obtain an improvement for Buckdahn's results established in Probab. Theory Related Fields 89 (1991), 211-238 and a generalization of Borell-TIS inequality. [ABSTRACT FROM AUTHOR]