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Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract The structural behaviour and design of hot-rolled and cold-formed steel continuous beams with square and rectangular hollow sections are studied in the present paper, with a focus on the beneficial effects of material strain hardening and moment redistribution. Finite element (FE) models were first developed and validated against existing test results on hot-rolled and cold-formed steel square and rectangular hollow section continuous beams. Upon validation against the experimental results, parametric studies were carried out to expand the available structural performance data over a range of cross-section geometries, cross-section slendernesses, steel grades and loading conditions. Representative material properties and residual stress patterns were incorporated into the FE models to reflect the two studied production routes – hot-rolling and cold-forming. The experimental results, together with the parametric numerical results generated herein, were then used to evaluate the accuracy of the design provisions of EN 1993-1-1 (2005) as well as the continuous strength method (CSM) for indeterminate structures, the latter of which is extended in scope in the present study. It was shown that the current provisions of EN 1993-1-1 (2005) for the design of hot-rolled and cold-formed steel continuous beams are rather conservative, while the proposed CSM yields a higher level of accuracy and consistency, due to its rational consideration of both strain hardening at the cross-sectional level and moment redistribution at the global system level. Finally, statistical analyses were carried out to assess the reliability level of the two design methods according to EN 1990 (2002). Highlights • Numerical models validated against test results for structural steel continuous beams. • Validated numerical models used to perform parametric studies considering key parameters. • Current design provisions in EN 1993-1-1 assessed using the experimental and numerical data. • The Continuous Strength Method extended to cover the design of structural steel continuous beams. • Reliability of the CSM evaluated by means of statistical analyses according to EN 1990. [ABSTRACT FROM AUTHOR]

Abstract Almost forty years after Turing's seminal paper on patterning, progress on modeling instabilities leading to pattern formation has been achieved. The initial concept of dissipative structure is now clearly understood within the Phase-Field framework. So far, such an approach obtained promising results in various aspects of materials research from pattern formation during solidification to defect dynamics. In this work, we will try discussing experimental results observed during aging of solids under irradiation within this framework. The approach followed in this presentation is comprehensive and not specialized in specific aspects of the Phase-Field modelling (mechanics, mathematics, or numerical methods) at the expense of a holistic picture. [ABSTRACT FROM AUTHOR]

For the interest of readers who do not need to deal with detailed mathematics, a succinct summary of the newly developed GSP N theory ( Chao, 2017 ) is given in this technical note. A streamlined presentation of the idea, concept, logic, formulation and the physics of the theory is given here such that the readers can more easily comprehend the overall picture and the explicit resulting equations to be used in implementation. The mathematical details are referred to the previous papers (Chao, 2016, 2017). All the relevant equations for the P 3 equivalent GSP 3 ( 3 ) theory are explicitly given. Issues of numerical implementation of the theory are discussed, and potentially viable methods are suggested and conceptually described. [ABSTRACT FROM AUTHOR]

In this paper, the underlying general linear methods (GLMs) are adapted to linear neutral multidelay-integro-differential equations (NMIDEs). In order to obtain stability criteria of the extended GLMs, the corresponding results in paper of Zhang and Vandewalle (2008) are generalized. Based on the concepts of A( α )-stability and A-stability of the underlying GLMs, a serial of asymptotic stability criteria of the extended GLMs are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we propose a theory for linear time fractional PDEs on L 2 ( R d ) , with two time parameters. The order of the time derivatives under consideration is less than 1. We study well-posedness, regularizing effects and dissipative properties. Regarding regularizing effects, we describe quite precisely the equations that have this effect or not. We highlight that, in purely fractional settings, the regularizing effect acts always only up to finite order; unlike to the standard case. Also, we investigate the properties of the three time variables solution operator generated by these PDEs. [ABSTRACT FROM AUTHOR]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

The Small Exponent Test (SET) for exponentiation is an essential batch-verification technique that is widely applied. In this paper, we propose a simplified SET that can securely batch-verify n instances with only n − 1 randomizing exponents. We show that the structure of the proposed batch test is compact in the sense that it works with a minimal number of randomizing exponents for the SET. Thus, our test offers various advantages. Overall, compared to the original SET, the proposed simplified SET is more efficient for any sized batch instance. In particular, unlike the SET, our proposal performs well even when the size of a batch instance is small, e.g., n = 1 , 2 , 3 , and 4. This feature can be also used to significantly reduce pairing computations in a signature scheme where several pairing equations are verified. In addition, our test can be combined easily and generically with existing batch techniques such as the use of sparse exponents, the bucket test for large batch sizes, or an automated tool to generate a batch algorithm. Finally, with our simplified test, an efficient identification algorithm can be constructed to discover incorrect instances in a batch. [ABSTRACT FROM AUTHOR]

A theorem of Hoischen states that given a positive continuous function ε : R n → R , an unbounded sequence 0 ≤ c 1 ≤ c 2 ≤ … and a closed discrete set T ⊆ R n , any C ∞ function g : R n → R can be approximated by an entire function f so that for k = 0 , 1 , 2 , …  , for all x ∈ R n such that | x | ≥ c k , and for each multi-index α such that | α | ≤ k , (a) | ( D α f ) ( x ) − ( D α g ) ( x ) | < ε ( x ) ; (b) ( D α f ) ( x ) = ( D α g ) ( x ) if x ∈ T . In this paper, we show that if C ⊆ R n + 1 is meager, A ⊆ R n is countable and disjoint from T , and for each multi-index α and p ∈ A we are given a countable dense set A p , α ⊆ R , then we can require also that (c) ( D α f ) ( p ) ∈ A p , α for p ∈ A and α any multi-index; (d) if x ∉ T , q = ( D α f ) ( x ) and there are values of p ∈ A arbitrarily close to x for which q ∈ A p , α , then there are values of p ∈ A arbitrarily close to x for which q = ( D α f ) ( p ) ; (e) for each α , { x ∈ R n : ( x , ( D α f ) ( x ) ) ∈ C } is meager in R n . Clause (d) is a surjectivity property whose full statement in the text also allows for finding solutions in A to equations of the form q = h ⁎ ( x , ( D α f ) ( x ) ) under similar assumptions, where h ( x , y ) = ( x , h ⁎ ( x , y ) ) is one of countably many given fiber-preserving homeomorphisms of open subsets of R n + 1 ≅ R n × R . We also prove a weaker corresponding result with “meager” replaced by “Lebesgue null.” In this context, the approximating function is C ∞ rather than entire, and we do not know whether it can be taken to be entire. The first result builds on earlier work of the author which deduced special cases of it from forcing theorems using absoluteness arguments. The proofs here do not use forcing. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear bending and vibration problems of functionally graded tubes with temperature-dependent material properties based on a refined beam model. The tubes are exposed to a uniform distributed temperature field and are placed on elastic foundation. The refined beam model for tubes can satisfy the stress boundary conditions on inner and outer surfaces. The governing equations of nonlinear bending and vibration for the functionally graded tubes are derived by using Hamilton's principle and are solved by introducing a two-step perturbation technique. Some comparisons for bending and vibration are presented to valid the correctness of present beam model and solution method. In numerical results, the effects of transverse shear deformation, the volume fraction, inner radius and elastic foundation stiffness as well as the temperature on the natural frequency, amplitude–frequency responses and nonlinear bending responses are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the solvability of interval matrix equations in max-plus algebra. Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a ⊕ b = max ⁡ { a , b } and a ⊗ b = a + b . The notation A ⊗ X ⊗ C = B represents an interval max-plus matrix equation, where A , B , and C are given interval matrices. We define four types of solvability of interval max-plus matrix equations, i.e., the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability. We derive the necessary and sufficient conditions for checking each of them, whereby all can be verified in polynomial time. [ABSTRACT FROM AUTHOR]

Tensor computation is intensive and difficult. Invariably, a vital component is the truncation of tensors, so as to control the memory and associated computational requirements. Various tensor toolboxes have been designed for such a purpose, in addition to transforming tensors between different formats. In this paper, we propose a simple Q-less QR truncation technique for tensors { x ( i ) } with x ( i ) ∈ R n 1 × ⋯ × n d in the simple and natural Kronecker product form. It generalizes the QR decomposition with column pivoting, adapting the well-known Gram–Schmidt orthogonalization process. The main difficulty lies in the fact that linear combinations of tensors cannot be computed or stored explicitly. All computations have to be performed on the coefficients α i in an arbitrary tensor v = ∑ i α i x ( i ) . The orthonormal Q factor in the QR decomposition X ≡ [ x ( 1 ) , ⋯ , x ( p ) ] = Q R cannot be computed but expressed as X R − 1 when required. The resulting algorithm has an O ( p 2 d n ) computational complexity, with n = max ⁡ n i . Some illustrative examples in the numerical solution of tensor linear equations are presented. [ABSTRACT FROM AUTHOR]

The Frequency Difference of Arrival (FDOA) equations derived in this paper are intended to increase the standard accuracy of the Low Earth Orbit (LEO) satellites dedicated to locate non-cooperative emitters placed on the Earth surface or in orbit about the Earth. The equations contain terms that are of the order of the corrections already taken into account in Navigation by GPS. In particular, two of them should not be neglected to this end, since they can be of the order of 10 − 10 . [ABSTRACT FROM AUTHOR]

Finding the solution of the absolute value equation (AVE) A x − | x | = b has attracted much attention in recent years. In this paper, we propose a relaxed nonlinear PHSS-like iterative method, which is more efficient than the Picard-HSS iterative method for the AVE, and is a generalization of the nonlinear HSS-like iteration method for the AVE. By using the theory of nonsmooth analysis, we prove the convergence of the relaxed nonlinear PHSS-like iterative method for the AVE. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the relaxed nonlinear HSS-like method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the discrete Legendre spectral Galerkin and discrete Legendre spectral collocation methods to approximate the solution of mixed type Hammerstein integral equation with smooth kernels. The convergence of the discrete approximate solutions to the exact solution is discussed and the rates of convergence are obtained. We have shown that, when the quadrature rule is of certain degree of precision, the rates of convergence for the Legendre spectral Galerkin and Legendre spectral collocation methods are preserved. We obtain superconvergence rates for the iterated discrete Legendre Galerkin solution. By choosing the collocation nodes and quadrature points to be same, we also obtain superconvergence rates for the iterated discrete Legendre collocation solution. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases, called the independently-based spaces. We show that first-countable spaces are precisely the independently-based, strongly Fréchet spaces and we give an example of a Fréchet–Urysohn space that is neither independently-based nor strongly Fréchet. [ABSTRACT FROM AUTHOR]

Abstract: A partition of unity method for the displacement obstacle problem of clamped Kirchhoff plates is considered in this paper. We derive optimal error estimates and present numerical results that illustrate the performance of the method. [Copyright &y& Elsevier]

The authors found some errors in their above titled paper which should be corrected in this Corrigendum. [ABSTRACT FROM AUTHOR]