In this paper, we present new upper and lower bounds for the spectral norms of the r-circulant matrices [Formula: see text] and [Formula: see text] whose entries are the biperiodic Fibonacci and biperiodic Lucas numbers, respectively. Finally, we obtain lower and upper bounds for the spectral norms of Kronecker and Hadamard products of Q and L matrices.

In this paper, we give upper and lower bounds for the spectral norms of circulant matrices A n = Circ(F n−1) and B n = Circ(L (k,h) n and L (k,h) n are the (k, h)-Fibonacci and (k, h)-Lucas numbers, then we obtain some bounds for the spectral norms of Kronecker and Hadamard products of these matrices.

envelopment analysis (dea) is a very eective method to evaluate the relative eciency of decision-making units (dmus). dea models divided all dmus in two categories: ecient and inecientdmus, and don't able to discriminant between ecient dmus. on the other hand, the observedvalues of the input and output data in real-life problems are sometimes imprecise or vague, suchas interval data, ...

The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....

Introduction: Facial beauty is becoming more and more important worldwide. This is defined as being close to what is advertised as attractiveness by the media and is determined mainly by golden proportions. This study aimed to observe the soft tissue facial angular and proportional norms of South Iranian population attending Shiraz Dental School’s clinic. Materials and methods: Seventy...

The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.

There are currently stimuli with published norms available to study several psychological aspects of language and visual cognitions. Norms represent valuable information that can be used as experimental variables or systematically controlled to limit their potential influence on another experimental manipulation. The present work proposes 480 photo stimuli that have been normalized for name, ca...

The aim of the present study was to provide Russian normative data for the Snodgrass and Vanderwart (Behavior Research Methods, Instruments, & Computers, 28, 516-536, 1980) colorized pictures (Rossion & Pourtois, Perception, 33, 217-236, 2004). The pictures were standardized on name agreement, image agreement, conceptual familiarity, imageability, and age of acquisition. Objective word frequenc...

T norms were introduced by Schweizer and Sklar see e g in the framework of probabilistic metric spaces and are based on a notion used by Menger in or der to extend the triangle inequality in the de nition of metric spaces towards probabilistic metric spaces They have been used extensively for de ning the in tersection of fuzzy sets and for modelling the logical and in fuzzy logic Continuous t n...