Firstly, in this paper, we apply the Fuzzy Restricted Variation Method to achieve an analytical and approximate unsymmetrical fuzzy solution for Fully Fuzzy Quadratic Equation. In this application, after finding the real root of 1-cut of $tilde{A}tilde{X}^{2}+tilde{B}tilde{X}+tilde{C}=tilde{D}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate soluti...

We consider the problem of classifying (possibly noncommutative) R-algebras of low rank over an arbitrary base ring R. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard involution. We then investigate a class of exceptional rings of degree 2 which occur in every rank n ≥ 1 and show that they essentially characterize all algeb...

We call a positive definite integral quadratic form universal if it represents all positive integers. Then Lagrange’s Four Square Theorem means that the sum of four squares is universal. In 1930, Mordell [M] generalized this notion to a 2-universal quadratic form: a positive definite integral quadratic form that represents all binary positive definite integral quadratic forms, and showed that t...

A simple plausibility argument is given. Let g be a finite-dimensional Lie algebra with generators J a and structure constants f ab c. The brackets are given by [J a , J b ] = f ab c J c. Denote the symmetric Killing metric (proportional to the quadratic Casimir operator) by δ ab = tr J a J b , and let the totally symmetric third Casimir operator be d abc = tr {J a , J b }J c .

This paper presents a hybrid procedure to solve Model Predictive Controller (MPC) for Piecewise Affine System (PWA) The approach presented here belong to the class of Branch and Bound (B&B) methods. The procedure uses the concepts of reachable set combined to the specific B&Bmethods, in order to reduce the number of Quadratic Problems (QP) needed to be solved by t he optimization algorithm. Cop...

We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying β2 = aβ + b with b dividing a, we give a necessary and sufficient condition for γ(β) = 1, i.e., that all rational numbers p/q ∈ [0, 1) with gcd(q, b) = 1 have a purely periodic β-expansion. A simple algorithm for determining the value of γ(β) for all quadratic Pisot numbers β is described.

We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along row...

ObjectiveExperts recommended that direct discharge without hospitalization (DDWH) for emergency departments (EDs) able to observe acute heart failure (AHF) patients should be >40%, and these discharged fulfil the following outcome standards: 30-day all-cause mortality <2% (outcome A); 7-day ED revisit due AHF < 10% B); revisit/hospitalization 20% C). We investigated outcomes in a nationwide coh...

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = accele...

For a set of integers A, we consider \(R(A)=\{a/b: a, b\in b\ne 0\}\). It is an open problem to study the denseness R(A) in p-adic numbers when A nonzero values attained by integral form. This has been answered for quadratic forms. Very recently, Antony and Barman have studied this diagonal binary cubic forms \(ax^3+by^3\), where b are integers. In article, We extend their results \(ax^n+by^n\)...