for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

Multi-instance learning (MIL) is a supervised where each example labeled bag with many instances. The typical MIL strategies are to train an instance-level feature extractor followed by aggregating instances features as bag-level representation information. However, such highly depends on large number of datasets, which difficult get in real-world scenarios. In this paper, we make the first att...

We present a complete list of the dimension 8 operator basis in standard model effective field theory using group theoretic techniques systematic and automated way. adopt new form operators terms irreducible representations Lorentz group, identify structures as states $SU(N)$ group. In this way, redundancy from equations motion is absent that integration-by-part treated fact independent forms a...

Problem statement: The widespread use of image, audio and video data makes media content protection increasingly necessary and important. We propose a naive approach which treats the multimedia signal to be protected as a text and use proposed encryption design to encrypt the whole data stream. Upon reception, the entire cipher text data stream would be decrypted and playback can be performed a...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

We consider rational functions of the form V(x)/U(x), where both V(x) and U(x) are relatively prime polynomials over finite field \(\mathbb {F}_q\). Polynomials that permute elements a field, called permutation (PPs), have been subject research for decades. Let \({\mathcal {P}}^1(\mathbb {F}_q)\) denote {F}_q\cup \{\infty \}\). If function, permutes {F}_q)\), it is function (PRF). \(N_d(q)\) nu...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

We formulate one dimensional many body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level. In one spatial dimension a class of integrable many-body systems is known, ref...