Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $|{\rm PSL}(2,p^2)|$ such that $G$ has an irreducible character of degree $p^2$ and we know that $G$ has no irreducible character $\theta $ such that $2p\mid \theta (1)$, then $G$ is isomorphic to ${\rm PSL}(2,p^2)$. As a consequence of our result we prove that ${\rm PSL}(2,p^2)$ is uniquely determined by the structure of its complex group algebra.
Let $\mu $ be a nonnegative Radon measure on ${{\mathbb R}^d}$ which only satisfies $\mu (B(x, r))\le C_0r^n$ for all $x\in {{\mathbb R}^d}$, $r>0$, with some fixed constants $C_0>0$ and $n\in (0,d].$ In this paper, a new characterization for the space $\mathop{\rm RBMO}(\mu )$ of Tolsa in terms of the John-Strömberg sharp maximal function is established.
Let $\Cal H$ be a separable infinite dimensional complex Hilbert space, and let $\Cal L(\Cal H)$ denote the algebra of all bounded linear operators on $\Cal H$ into itself. Let $A=(A_{1},A_{2},\dots ,A_{n})$, $B=(B_{1},B_{2},\dots ,B_{n})$ be $n$-tuples of operators in $\Cal L(\Cal H)$; we define the elementary operators $\Delta_{A,B}\:\Cal L(\Cal H)\mapsto\Cal L(\Cal H)$ by $\Delta_{A,B}(X)=\sum_{i=1}^nA_iXB_i-X.$ In this paper, we characterize the class of pairs of operators $A,B\in\Cal L(\Cal H)$ satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators $A,B\in\Cal L(\Cal H)$ such that $\sum_{i=1}^nB_iTA_i=T$ implies $\sum_{i=1}^nA_i^*TB_i^*=T$ for all $T\in\Cal C_1(\Cal H)$ (trace class operators). The main result is the equivalence between this property and the fact that the ultraweak closure of the range of the elementary operator $\Delta_{A,B}$ is closed under taking adjoints. This leads us to give a new characterization of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel in $C_1$ classes.
Let G be a group and !(G) be the set of element orders of G. Let k 2 !(G) and mk(G) be the number of elements of order k in G. Let nse(G) = {mk(G) : k 2 !(G)}. Assume r is a prime number and let G be a group such that nse(G) = nse(Sr), where Sr is the symmetric group of degree r. In this paper we prove that G = Sr, if r divides the order of G and r2 does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components., Azam Babai, Zeinab Akhlaghi., and Seznam literatury
In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.
We present a new Generalized Learning Vector Quantization classifier called Optimally Generalized Learning Vector Quantization based on a novel weight-update rule for learning labeled samples. The algorithm attains stable prototype/weight vector dynamics in terms of estimated current and previous weights and their updates. Resulting weight update term is then related to the proximity measure used by Generalized Learning Vector Quantization classifiers. New algorithm and some major counterparts are tested and compared for synthetic and publicly available datasets. For both the datasets studied, it is seen that the new classifier outperforms its counterparts in training and testing with accuracy above 80% its counterparts and in robustness against model parameter varition.
We present an hitherto unknown cometary reflection nebula {a = 20^h18^m3, δ+37°00') associated with a dense dust cloud. A bright, compact Herbig-Haro oject is embedded in its brightest part. The highly reddened illuminating star of about 3-5 M„, located near the apex of the nebula, emits a collimated bipolar flow at high velocity, whose blueshifted stream feeds the HH object. The redshifted stream can be traced toward the interior of the dark cloud, where the density exceeds 10^5 cm^-3.
We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem., Márcia Federson, Jaqueline Godoy Mesquita., and Obsahuje seznam literatury
In this paper, a new adjustment to the damping parameter of the Levenberg-Marquardt algorithm is proposed to save training time and to reduce error oscillations. The damping parameter of the Levenberg-Marquardt algorithm switches between a gradient descent method and the Gauss-Newton method. It also affects training speed and induces error oscillations when a decay rate is fixed. Therefore, our damping strategy decreases the damping parameter with the inner product between weight vectors to make the Levenberg-Marquardt algorithm behave more like the Gauss-Newton method, and it increases the damping parameter with a diagonally dominant matrix to make the Levenberg-Marquardt algorithm act like a gradient descent method. We tested two simple classifications and a handwritten digit recognition for this work. Simulations showed that our method improved training speed and error oscillations were fewer than those of other algorithms.