The present paper considers the wire drawing process through a conical die and provides an approximate solution for force, assuming arbitrary hardening law. is based on upper bound theorem. However, this theorem does not apply to stationary flow of strain-hardening materials. Therefore, adopted engineering approach replace original material model with non-homogeneous, perfectly plastic model. k...

Gallager bound is known as the minimum upper bound of average error probability of classical channel coding[5]. Burnashev and Holevo[8] derived its quantum version in the pure states case, and proposed its quantum version in the mixed states case. The attainability of their quantum version has been an open problem, We prove that the bound proposed by them can be attained by a POVM proposed by H...

We start with a result showing most odd cubes cannot be perfect numbers (see Theorem 1). Then we give a new proof of a special case of a result of Iannucci (see [IAN]) that shows that none of the even exponents in N ’s prime factorization can be congruent to 4 (mod 5) if 3|N (Theorem 2). We then extend that result by proving that certain sets of small primes, when taken to a large power, cannot...

Suppose that M is a compact Riemannian manifold with boundary and u is an L-normalized Dirichlet eigenfunction with eigenvalue λ. Let ψ be its normal derivative at the boundary. Scaling considerations lead one to expect that the L norm of ψ will grow as λ1/2 as λ → ∞. We prove an upper bound of the form ‖ψ‖ 2 ≤ Cλ for any Riemannian manifold, and a lower bound cλ ≤ ‖ψ‖ 2 provided that M has no ...

The purpose of this paper is to present a method for calculating the upper bound limit loads plate bending using conforming Hsieh-Clough-Tocher (HCT) element. These can be obtained from Koiter’s kinematic shakedown theorem case one load vertex instead theorem. When combining with approximated displacement field, analysis turns into an optimization problem and effectively solved by Second-Order ...

We show that assuming lower bounds on the Ricci curvature and injectivity radius absolute value of certain characteristic numbers a Riemannian manifold, including all Pontryagin Chern numbers, is bounded proportionally to volume. The proof relies Chern–Weil theory applied connection constructed from Euclidean connections charts in which metric tensor harmonic has Hölder norm. generalize this th...

The following combinatorial theorems, some of which were known for every finite n in all infinite structures, are proved in ZFC for every infinite cardinal ν in all sufficiently large structures. (a) A new extension of Miller’s theorem [18]. (b) An upper bound of ρ on the list-conflict-free number of ρ-uniform families of sets which satisfy C(ρ, ν) for cardinals ν and ρ ≥ iω(n). (c) An upper bo...

Szegö’s theorem states that the asymptotic behavior of the eigenvalues of a Hermitian Toeplitz matrix is linked to the Fourier transform of its entries. This result was later extended to block Toeplitz matrices, i.e., covariance matrices of multivariate stationary processes. The present work gives a new proof of Szegö’s theorem applied to block Toeplitz matrices. We focus on a particular class ...

Following Ohtsuki, Garoufalidis, and Habegger we provide an elementary introduction to nite type invariants of integral homology spheres, culminating with a proof of the upper bound for the magnitude of the space I of such invariants in terms of the space A(;) of oriented trivalent graphs modulo the so-called AS and IHX relations. We raise the issue of \the fundamental theorem" for nite type in...

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate via certain Monte Carlo simulations. main results represent upper bound errors between exact solution and approximation, estimate fluctuation appropriate central limit theorem (CLT) construction confidence intervals. Moreover, provide rates convergence ...