求∂‖A∘(Y−W⊤X)‖F2∂W和∂‖A∘(Y−W⊤X)‖F2∂X,其中,∘表示Hadamard product,各变量均为矩阵形式。 求解: 为方便起见,定义Z=A∘(Y−W⊤X),同时,将F-norm重写为Frobenius product(详见备注)的形式,则有: ∂‖A∘(Y−W⊤X)‖F2=∂Z:Z=2Z:dZ=2Z:d(A∘...
This inequality is then applied to study the stability of neural network systems of Hopfield type. To this end, we establish some properties like the Hadamard derivative of the product of two functions and the permutation of the Hadamard derivative and the integral or the Hadamard derivative of ...
The superposition states are simply obtained by applying a Hadamard gate to each qubit. Hadamard transform has a unitary operator as (11.16)H=12[111−1]. For a single qubit with a state of |ψ〉=a|0〉+b|1〉, the Hadamard gate produces the following results: (11.17)H|ψ〉=12[111...
In this paper, we have introduced and investigated a new subclass of multivalent functions by using the Hadamard product structure to obtain new linear operator involving Ruscheweyh derivative that defined in the open unit disk. We have ob- tained coefficient estimates, distortion theorem, inclusion...
Hadamard product (or convolution)q-Derivative (orq-Difference) operatorq-Analogue of Ruscheweyh’s derivative operatorDifferential subordinationIn the present paper, by using the concept of convolution and q -calculus, we define a certain q -derivative (or q -difference) operator for analytic and...
Some interesting properties and characteristics of the Hurwitz-Lerch Zeta function Φ(z, s, b) can be found in [5], =-=[10]-=-, [11], [13] and [19]. Recently, Srivastava and Attiya [18] introduced the linear operator Js,b : A → A, defined in terms of the Hadamard product,...
analytic functionsHadamard productRuscheweyh derivativeintegral operatorsIn the paper are studied the properties of the image of a class of analytic functions defined by the Ruscheweyh derivative trough the Bernardi operator.doi:10.1515/ausm-2015-0019Ágnes Orsolya Páll-Szabó...
Given two functions f, g A, where f (z) is given by (1.1) and g(z) is given by g(z) = z + The Hadamard product f and g, denoted by f*g and is defined by f*g(z) = z + The Ruscheweygh derivative of order k is denoted by Dkf and is defined as follows: If f(z) ...
Convolution (or Hadamard productThe purpose of this present effort is to define a new fractional differential operatorTzβ,τ,γ, involving Srivastava–Owa fractional derivative operator. Further, we investigate some geometric properties such as univalency, starlikeness, convexity for their normalization,...
Introduction Fractional derivative (FD) is the name assigned to several mathematical operators, namely the Grünwald-Letnikov (GL), Liouville (L), Riemann-Liouville (RL), Caputo (C), Marchaud, Hadamard, Riesz, and other definitions [1–7]. Nevertheless, there is a long standing debate about ...