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The Z-function is the real function given by Z (t) = e i θ (t) ζ 1 2 + i t , where ζ (s) is the Riemann zeta function, and θ (t) is the Riemann–Siegel theta function. The function, central to the study of the Riemann hypothesis (RH), has traditionally posed significant computational challenges. This research addresses these challenges by exploring new methods for approximating Z (t) and its zeros. The sections of Z (t) are given by Z N (t) : = ∑ k = 1 N cos (θ (t) − ln (k) t) k for any N ∈ N . Classically, these sections approximate the Z-function via the Hardy–Littlewood approximate functional equation (AFE) Z (t) ≈ 2 Z N ˜ (t) (t) for N ˜ (t) = t 2 π . While historically important, the Hardy–Littlewood AFE does not sufficiently discern the RH and requires further evaluation of the Riemann–Siegel formula. An alternative, less common, is Z (t) ≈ Z N (t) (t) for N (t) = t 2 , which is Spira's approximation using higher-order sections. Spira conjectured, based on experimental observations, that this approximation satisfies the RH in the sense that all of its zeros are real. We present a proof of Spira's conjecture using a new approximate equation with exponentially decaying error, recently developed by us via new techniques of acceleration of series. This establishes that higher-order approximations do not need further Riemann–Siegel type corrections, as in the classical case, enabling new theoretical methods for studying the zeros of zeta beyond numerics. [ABSTRACT FROM AUTHOR]

For the solid-on-solid (SOS) model with an external field and with spin values from the set of all integers on a Cayley tree, each (gradient) Gibbs measure corresponds to a boundary law (an infinite-dimensional vector function defined on vertices of the Cayley tree) satisfying a nonlinear functional equation. Recently some translation-invariant and height-periodic (non-normalizable) solutions to the equation are found. Here, our aim is to find non-height-periodic and non-normalizable boundary laws for the SOS model. By such a solution one can construct a non-probability Gibbs measure. We find explicitly several non-normalizable boundary laws. Moreover, we reduce the problem to solving of a nonlinear, second-order difference equation. We give analytic and numerical analyses of the difference equation. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic rules for the numerical solution of Hammerstein integral equation based on spline quasi-interpolant. Also the convergence analysis of the methods are given. The theoretical behavior is tested on examples and it is shown that the numerical results confirm theoretical part. [ABSTRACT FROM AUTHOR]

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence. [ABSTRACT FROM AUTHOR]

Abstract The Arnold–Beltrami–Childress (ABC) flow is the best-known example of a Beltrami flow (or a force-free field in plasma physics) periodic in three orthogonal directions. When its three parameters are equalised, its set of streamlines has the same crystallographic symmetry as a model of a blue phase (BP) of cholesteric liquid crystals. This commonality appears in the similarity between the arrangements of invariant tori in the ABC flow and of double-twist cylinders in the BP model. In this paper, three Beltrami flows whose sets of streamlines have the same crystallographic symmetries as three other BP models are derived by using cubic space groups. The first and the third Beltrami flows have invariant tori arranged similarly to double-twist cylinders in two of the BP models. The second Beltrami flow has invariant tori whose arrangement has been neither theoretically nor experimentally known in liquid crystals. Heteroclinic orbits in the three flows are also studied. [ABSTRACT FROM AUTHOR]

Abstract Two different wdf (wall-distance-free) approaches are devised using local wall-distance and dissipation based representations to obtain consistency formulations for blending functions associated with the SST model. The strain-dependent coefficient C ̄ μ assists the SST model in constructing the functions such as to benefit complex flows with non-equilibrium turbulence, while retaining the predictive quality of unmodified SST closure. Naturally, the proposed methods allow the original SST model to be modified accurately and alleviate the free-stream dependency. Comparisons with the original SST k - ω model demonstrate that the newly developed alternatives to actual wall-distance usually improve the response of SST model to non-equilibrium effects. [ABSTRACT FROM AUTHOR]

Packing and covering linear programs (PC-LP s) form an important class of linear programs (LPs) across computer science, operations research, and optimization. Luby and Nisan (in: STOC, ACM Press, New York, 1993) constructed an iterative algorithm for approximately solving PC-LP s in nearly linear time, where the time complexity scales nearly linearly in N, the number of nonzero entries of the matrix, and polynomially in ε , the (multiplicative) approximation error. Unfortunately, existing nearly linear-time algorithms (Plotkin et al. in Math Oper Res 20(2):257–301, 1995; Bartal et al., in: Proceedings 38th annual symposium on foundations of computer science, IEEE Computer Society, 1997; Young, in: 42nd annual IEEE symposium on foundations of computer science (FOCS'01), IEEE Computer Society, 2001; Koufogiannakis and Young in Algorithmica 70:494–506, 2013; Young in Nearly linear-time approximation schemes for mixed packing/covering and facility-location linear programs, 2014. arXiv:1407.3015; Allen-Zhu and Orecchia, in: SODA, 2015) for solving PC-LP s require time at least proportional to ε - 2 . In this paper, we break this longstanding barrier by designing a packing solver that runs in time O ~ (N ε - 1) and covering LP solver that runs in time O ~ (N ε - 1.5) . Our packing solver can be extended to run in time O ~ (N ε - 1) for a class of well-behaved covering programs. In a follow-up work, Wang et al. (in: ICALP, 2016) showed that all covering LPs can be converted into well-behaved ones by a reduction that blows up the problem size only logarithmically. [ABSTRACT FROM AUTHOR]

A parity time-reversal duality symmetric structure constituted by a perfect electric conductor and perfect magnetic conductor (PMC) parallel plate waveguide is analyzed. This waveguide supports unimodal transverse electromagnetic (TEM) edge mode propagation protected against backscattering from a certain class of deformations and defects. The TEM solution is found in analytical form by using three different methods, namely, conformal mapping, mode-matching, and Fourier-transform methods. It is shown through numerical simulations that the mode propagation is robust with respect to deformations such as 90° bends and discontinuities such as transition to free space. Implementation of the PMC boundary conditions via both a bed of nails and a mushroom structure is also successfully investigated. [ABSTRACT FROM AUTHOR]

Classical scope-assignment strategies for multi-quantifier sentences involve quantifier phrase (QP)-movement (e.g., [11], [12]). More recent continuation-based approaches provide a compelling alternative, for they interpret QPs in situ -- without resorting to Logical Forms or any structures beyond the overt syntax. The continuation-based strategies can be divided into two groups: those that locate the source of scope-ambiguity in the rules of semantic composition (e.g., [1]) and those that attribute it to the lexical entries for the quantifier words (e.g., [2], [8]). In this paper, we focus on the former operation-based approaches and the nature of the semantic operations involved. More specifically, we discuss three such possible operation-based strategies for multi-quantifier sentences, together with their relative merits and costs. [ABSTRACT FROM AUTHOR]

We prove the higher differentiability and the higher integrability of the a priori bounded local minimizers of integral functionals of the form ℱ ⁢ (v , Ω) = ∫Ωƒ⁢ (x, Dv(x))dx, with convex integrand satisfying p-growth conditions with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x-variable belongs to a suitable Sobolev space. The a priori boundedness of the minimizers allows us to obtain the higher differentiability under a Sobolev assumption which is independent on the dimension n and that, in the case p ≤ n −2, improves previous known results. We also deal with solutions of elliptic systems with discontinuous coefficients under the so-called Uhlenbeck structure. In this case, it is well known that the solutions are locally bounded and therefore we obtain analogous regularity results without the a priori boundedness assumption. [ABSTRACT FROM AUTHOR]

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families. [ABSTRACT FROM AUTHOR]

In precast concrete segmental tunnels, radial and circumferential joints are often the most highly stressed parts and it is therefore important to use appropriate equations to accurately analysed these joints during design and provide adequate structural capacity to avoid failure. Different design codes have put forward equations for the estimation of bursting forces due to concentrated load on precast end blocks. The equations were specifically developed for pre-stressed concrete anchors and not specifically for precast concrete segmental tunnels. The design equations often account for the effects of load eccentricity in estimating bursting force but not the peak stress. This paper assesses the accuracy of published equations for bursting force and peak stress by conducting a high-resolution two-dimensional (2D) finite element (FE) based parametric studies. It was found that the effects of load eccentricity are significant for highly concentrated loads (load width ratios less than 0.3) and that they increase the peak bursting stresses significantly. Regression analysis is used to develop equations for estimating the peak bursting stress and bursting force due to load eccentricity for the design of precast concrete tunnel segments. These equations are more accurate as compared to pre-existing equations and important for practising engineers and designers. [ABSTRACT FROM AUTHOR]

Free vibration of a bimaterial circular nano-tube is investigated. The tube is formed by bonding together a Si3N4/SUS304 functionally graded upper semi tube and a ZrO2/Ti-6Al-4V functionally graded lower semi tube. The material properties of the tube are assumed to vary along the radius according to power law with the power index of upper semi tube differing from that of lower semi tube. Based on non-local elasticity theory and Hamilton's principle, a refined beam model considering the effect of transverse shear deformation is used to derive the governing equations, then analytical solution is obtained by using a two-steps perturbation method. Our results were compared with the existing ones. The effects on tube's linear and non-linear frequency are analyzed of the factors, including small scale parameter, temperature, the double volume fraction indexes, slenderness ratio and different types of beam model. A new approach is suggested in this article to change the natural frequency of the tubes by adjusting constituent materials. In contrast to conventional approach, the new one can result in more accurate frequency control in the same dimensionless size of tubes. [ABSTRACT FROM AUTHOR]

Multi-bolted joints are adopted and designed to provide efficient load transfer within assembled engineering parts. Bearing failure is favorable during design phase due to more progressive failure mode, however, ability of by-pass stress to be transferred to adjacent bolts in multi-bolted joints prone to catastrophic net-tension failure. Former approach known as equivalent spring stiffness (ESS) was proposed but it requires experimental sliding load value. This has led to semi-empirical approach to require experimental set-up than incorporating a generic bolt preload value. This paper aims to provide a unified bolt preload (UBP) value to be implemented in each bolt independent upon plate properties and bolts arrangements. Strength prediction were taken place by 3-D Extended Finite Element Method (XFEM) framework of various staggered and non-staggered arrangements to include various lay-ups types and plate thickness. The failure loads predictions in each testing series were investigated and then validated against experimental datasets and also compared with previous technique (ESS approach). Crack patterns and failure modes from this approach were consistent with experimental observations, where net-tension failures were observed within all testing series. Less good prediction compared to from ESS technique, partly due to semi-empirical nature in former approach. Nevertheless, reasonable agreement in UBP technique with experimental datasets were obtained (average discrepancy of approximately 20%). [ABSTRACT FROM AUTHOR]

We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler–Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi's theorem on conjugate points and Noether's theorem. We close with an application to low regularity Riemannian geometry. [ABSTRACT FROM AUTHOR]

In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently. [ABSTRACT FROM AUTHOR]

We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems. Based on the spectral analysis for the Lax pair formulation, we show that the spectral functions can be characterized from the boundary values. We express the solution of the equation in terms of the unique solution of the matrix Riemann–Hilbert problem whose jump matrices are defined by the spectral functions. Moreover, we derive the global algebraic relation that involves the boundary values. In addition, it can be verified that the solution of the elliptic sinh-Gordon equation posed in the semi-strip exists if the spectral functions defined by the boundary values satisfy this global relation. [ABSTRACT FROM AUTHOR]

In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (−Δp)su = λu−q + uα, u > 0 in ⁢ Ω, u = 0 in ⁢ ℝn∖Ω, where Ω is a bounded domain in ℝnwith smooth boundary ∂Ω, n > sp, s ∈ (0, 1), λ > 0, 0 < q ≤ 1 and 1 < p < α + 1 ≤ ps*. We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ. [ABSTRACT FROM AUTHOR]

We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations, du/dt (t) ∈ A(t)u(t), t ≥ 0, u(0) = u0, and their whole line analogues, du/dt (t) ∈ A(t)u(t), t ∈ ℝ, with a family {A(t)}t ∈ ℝ of ω-dissipative operators A (t) ⊂ X × X in a general Banach space X. According to the classical DeLeeuw–Glicksberg theory, functions of various generalized almost periodic types uniquely decompose in a "dominating" and a "damping" part. The second main object of the study – in the above context – is to determine the corresponding "dominating" part [A ⋅)]a(t) of the operators A(t), and the corresponding "dominating" differential equation, du/dt (t) ∈ [A(⋅)]a(t)u(t), t ∈ ℝ. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the following problem: { (−Δ)p,βs⁢u = ƒ(x,u) in⁢ Ω, u = 0 in ⁢ ℝN∖Ω , where Ω is a smooth bounded domain of ℝN containing the origin, (−Δ)p,βs⁢u(x) := PV ⁢ ∫ℝN |u⁢(x) − u(y)|p−2(u(x) − u(y))/|x − y|N+p⁢s⁢ dy/|x|β|y|β with 0 ≤ β < N−p⁢s/2, 1 < p < N, s ∈ (0 , 1), and ps < N. The main purpose of this work is to prove the existence of a weak solution under some hypotheses on ƒ. In particular, we will consider two cases: (i) ƒ(x, σ) = ƒ(x); in this case we prove the existence of a weak solution, that is, in a suitable weighted fractional Sobolev space for all ƒ ∈ L1(Ω). In addition, if ƒ ⪈ 0, we show that the problem above has a unique entropy positive solution. (ii) ƒ(x, σ) = λσq + g(x), σ ≥ 0; in this case, according to the values of λ and q, we get the largest class of data g for which the problem above has a positive solution. [ABSTRACT FROM AUTHOR]

We consider the non-local operator of variable order as follows: Lf(x) = ... (f(x + z) -- f(x) -- (∇ f(x), z) 1{|z|≤1})n(x, z)/... dz, where α(x) ∈ [α0, α2] for any x ∈ Rd and some constants 0 < α0 ≤ α2 < 2 and n(x, z) is a positive Borel measurable function bounded from above and below. Under mild continuity conditions on α(x) and n(x, z), we establish the H¨older regularity for the associated semigroups. The proof is based on a new construction of the coupling by reflection for non-local operator L, and the results successfully apply to both stable-like processes in the sense of Bass and time-change of symmetric stable processes. [ABSTRACT FROM AUTHOR]

This paper aims to address a new version of Newton's method for solving constrained generalized equations. This method can be seen as a combination of the classical Newton's method applied to generalized equations with a procedure to obtain a feasible inexact projection. Using the contraction mapping principle, we establish a local analysis of the proposed method under appropriate assumptions, namely metric regularity or strong metric regularity and Lipschitz continuity. Metric regularity is assumed to guarantee that the method generates a sequence that converges to a solution. Under strong metric regularity, we show the uniqueness of the solution in a suitable neighborhood, and that all sequences starting in this neighborhood converge to this solution. We also require the assumption of Lipschitz continuity to establish a linear or superlinear convergence rate for the method. [ABSTRACT FROM AUTHOR]

Using explicit methods, we provide an upper bound to the norm of the Busemann cocycle of a locally finite regular tree X, emphasizing the symmetries of the cocycle. The latter takes value into a submodule of square summable functions on the edges of X, which corresponds to the Steinberg representation for rank one groups acting on their Bruhat-Tits tree. The normof the Busemann cocycle is asymptotically linear with respect to square root of the distance between any two vertices. Independently, Gournay and Jolissaint [10] proved an exact formula for harmonic 1-cocycles covering the present case. [ABSTRACT FROM AUTHOR]

The study of quantum integers and their operations is closely related to the studies of symmetries of roots of polynomials and of fundamental questions of decompositions in Additive Number Theory. In his papers on quantum arithmetics, Melvyn Nathanson raises the question of classifying solutions of functional equations arising from the multiplication of quantum integers, starting with polynomial solutions and then generalizing to rational function solutions. The classification of polynomial solutions with fields of coefficients of characteristic zero and support base P has been completed. In a paper concerning the Grothendieck group associated to the collection of polynomial solutions, Nathanson poses a problem which asks whether the set of rational function solutions strictly contains the set of ratios of polynomial solutions. It is now known that there are infinitely many rational function solutions Γ with fields of coefficients of characteristic zero not constructible as ratios of polynomial solutions, even in the purely cyclotomic case, which is the case most similar to the polynomial solution case. The classification of polynomial solutions is thus not sufficient, in essential ways, to resolve the classification problem of all rational function solutions with fields of coefficients of characteristic zero. In this paper we study symmetries of roots of rational functions and the classification of the important class-the last and main obstruction to the classification problem-of rational function solutions, the purely cyclotomic, purely nonrational primitive solutions with fields of coefficients of characteristic zero and support base P, which allows us to complete the classification problem raised by Nathanson. [ABSTRACT FROM AUTHOR]

In this work, the static stability of a thin plate in axial subsonic airflow is studied using the framework of Possio integral equation. Specifically, we consider the cases when the plate’s leading edge is free and the plate’s trailing edge is either pinned or clamped. We formulate the problem under consideration using a partial differential equations (PDE) model and then linearize the model about the free stream velocity, density, and pressure, to enable analytical treatment. Based on the linearized model, we introduce a new derivation of a Possio integral equation that relates the pressure jump along the thin plate to the plate’s downwash. The steady state solution to the Possio equation is then used to account for the aerodynamic loads in the plate steady state governing equation resulting in a singular differential-integral equation which is transformed to a singular integral equation that represents the static aeroelastic equation of the plate. We verify the solvability of the static aeroelastic equation based on the Fredholm alternative for compact operators in Banach spaces and the contraction mapping theorem. By constructing solutions to the static aeroelastic equation and matching the nonzero boundary conditions at the trailing edge with the zero boundary conditions at the leading edge, we obtain characteristic equations for the free-clamped and free-pinned plates. The minimum solutions to the characteristic equations are the divergence speeds which indicate when static instabilities start to occur. We show analytically that free-pinned plates are statically unstable. We also construct, analytically, flow speed intervals that correspond to static stability regions for free-clamped plates. Furthermore, we resort to numerical computations to obtain an explicit formula for the divergence speed of free-clamped plates. Finally, we apply the obtained results on piezoelectric plates and we show that free-clamped piezoelectric plates are statically more stable than conventional free-clamped plates due to the piezoelectric coupling. [ABSTRACT FROM AUTHOR]

Stochastic differential equation has accumulated a large number of bases in numeral analysis over decades of development. It can accurately and truly reflect some development rules in the fields such as economics, physics and astronomy when being applied in practice. Stability of numeral solution is the key in numerical analysis of stochastic differential equation. In this study, the stability of numeral solution of stochastic differential equation was discussed and verified. Nonlinear stochastic equation was solved using stochastic-θ method under general decay rate, and two sufficient conditions were proposed for the obtained numerical solutions. It was verified that the numeral solution obtained using stochastic-θ method was p-th moment Φ(t)-stable and almost surely Φ(t)-stable under the sufficient conditions. [ABSTRACT FROM AUTHOR]

Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions f : G → C of the functional equation ∫G f (σ(y)xt)dμ(t) + ∫G f (xyt)dν(t) = f (x)f (y), x,y ∈ G, in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d'Alembert's, Cauchy's, Gajda's, Kannappan's, Stetkær's, Van Vleck's equations...). So, a large class of functional equations will be solved. [ABSTRACT FROM AUTHOR]

We propose several circulant preconditioners for systems defined by some functions g of Toeplitz matrices A n . In this paper we are interested in solving g ( A n ) x = b by the preconditioned conjugate method or the preconditioned minimal residual method, namely in the cases when g ( z ) are the functions e z , sin ⁡ z and cos ⁡ z . Numerical results are given to show the effectiveness of the proposed preconditioners. [ABSTRACT FROM AUTHOR]

This paper deals with variational inclusions of the form 0∈K−f(x) where f:Rn→Rm is a semismooth function and K is a nonempty closed convex cone in Rm. We show that the previous problem can be solved by a Newton-type method using the Clarke generalized Jacobian of f. The results obtained in this paper extend those obtained by Robinson in the famous paper (Robinson in Numer. Math. 19:341-347, 1972). We provide a semilocal method with a superlinear convergence that is new in the context of semismooth functions. Finally, numerical results are also given to illustrate the convergence. [ABSTRACT FROM AUTHOR]

In this paper, we give the solution of a problem formulated in Kominek and Sikorska (Aequationes Math 90:107-121, 2016) in connection with the functional equation f(xy)-f(x)-f(y)=g(x+y)-g(x)g(y).Our result can also be interpreted in the way that, under some additional condition, the logarithmic and the exponential Cauchy equations are strongly alien. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is presented to solve functional Hammerstein integro-differential equations. The presented method combines the successive approximations method with trapezoidal quadrature rule and natural cubic spline interpolation to solve the mentioned equations. The existence and uniqueness of the problem is also investigated. The convergence and numerical stability of the problem are proved, and finally, the accuracy of the method is verified by presenting some numerical computations. [ABSTRACT FROM AUTHOR]

Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations. [ABSTRACT FROM AUTHOR]

In this paper, it will be generalized the notion of hypergroups of type U on the right to ternary hypergroups of type U on the right and some of their properties will be investigated. We will determine all ternary hypergroups of size 2 and 3. Quotient ternary hypergroups of type U on the right, by defining a regular relation, are considered and it will be proved that arisen ternary hypergroup is right reversible. [ABSTRACT FROM AUTHOR]

This paper shows that every finite non-degenerate involutive set theoretic solution ( X , r ) of the Yang–Baxter equation whose permutation group G ( X , r ) has cardinality which is a cube-free number is a multipermutation solution. Some properties of finite braces are also investigated. It is also shown that if A is a left brace whose cardinality is an odd number and ( − a ) ⋅ b = − ( a ⋅ b ) for all a , b ∈ A , then A is a two-sided brace and hence a Jacobson radical ring. It is also observed that the semidirect product and the wreath product of braces of a finite multipermutation level is a brace of a finite multipermutation level. [ABSTRACT FROM AUTHOR]

In this current work, we acquire the general solution and Hyers-Ulam stability for a new form of Quattuorvigintic functional equation in Matrix Paranormed Space by using the direct and fixed point methods. [ABSTRACT FROM AUTHOR]

We live in a world powered by information. This truth gives us the potential to master as much information as we can in order to make our activity more efficient. The development of technology gives us both the means and the capabilities to gather and analyze this large amount of information so that we can use more efficiently the limited resources that we dispose of. Basically, this paper presents a modality of modelling smart university and smart enterprise environments based on the principles of System Dynamics, the model of economic map presented in previous papers and the concept of smartness within an environment. In these terms, smart is referred to the usage of new methodologies and technologies in order to optimize the activity in a controlled economy-based or educational environment. [ABSTRACT FROM AUTHOR]

Let F ( x , y , z ) be a hyperbolic ternary form of degree n . The Helton–Vinnikov theorem asserts that there exists an n × n complex symmetric matrix S such that F S ( x , y , z ) = F ( x , y , z ) , where the determinantal hyperbolic ternary form of an n × n matrix B is defined by F B ( x , y , z ) = det ⁡ ( x ℜ ( B ) + y ℑ ( B ) + z I n ) . Let A be an n × n unitary bordering matrix. It is known that A is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity between the unitary bordering matrix A and the Helton–Vinnikov symmetric matrix S admitted the determinantal representation of the ternary form F A ( x , y , z ) satisfying F S ( x , y , z ) = F A ( x , y , z ) for n = 3 , 4 . [ABSTRACT FROM AUTHOR]

In this paper, we show that an infinite lower triangular matrix A = [ a i j ] i , j ∈ N 0 is an exponential Riordan matrix A = E ( g , f ) given by ∑ i ≥ j a i j z i / i ! = g f j / j ! if and only if there exist both a horizontal pair { h n ; h ˜ n } n ≥ 0 and a vertical pair { v n ; v ˜ n } n ≥ 0 of sequences that represent all the elements in the matrix. As a consequence, we obtain that if the horizontal and vertical pairs of an exponential Riordan matrix are identical then the matrix is an involution. In addition, this concept can be applied to obtain the determinants of the production matrix and some conditions for the d -orthogonality of the Sheffer polynomial sequences. [ABSTRACT FROM AUTHOR]

We describe an algorithm for the numerical solution of second order linear ordinary differential equations in the high-frequency regime. It is based on the recent observation that solutions of equations of this type can be accurately represented using nonoscillatory phase functions. Unlike standard solvers for ordinary differential equations, the running time of our algorithm is independent of the frequency of oscillation of the solutions. We illustrate this and other properties of the method with several numerical experiments. [ABSTRACT FROM AUTHOR]

We introduce and investigate the family of partially directed snake polyominoes. We first present a classification of snake polyominoes and then we turn our attention on the class of partially directed snakes. We establish recurrences, functional equations and generating functions with respect to length and height for two dimensional, three dimensional and d dimensional partially directed snake polyominoes. We then inscribe partially directed snake polyominoes in a b × h rectangle. In order to include the third variable b in our study, we trade the parameter b for two variables w , v to obtain recurrences and functional equations with four variables. We investigate subfamilies of partially directed snake polyominoes. One of these families extends to Z d . In particular, we show a bijective relation between the subfamily of bubble polyominoes and bargraph polyominoes. [ABSTRACT FROM AUTHOR]

In [36], Park proved the Hyers-Ulam stability of set-valued functional equations by using the direct method. In this paper, we prove the Hyers-Ulam stability of set-valued functional equations by using the fixed point method. [ABSTRACT FROM AUTHOR]