scholarly journals On Recognizability of Groups by Bottom Layer

2020 ◽  
Vol 57 (1-4) ◽  
pp. 1-5
Author(s):  
Vladimir Senashov ◽  
Ivan Parashchuk
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Prime Order ◽  
Bottom Layer ◽  
Group A

The bottom layer of a group is a set of its elements of prime order. A group is called recognizable by bottom layer under additional conditions if it is uniquely restored by bottom layer under these conditions. A group is called almost recognizable by bottom layer under additional conditions, if there are a finite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. A group is called unrecognizable by bottom layer under additional conditions if there are an infinite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. In the paper we consider examples of groups recognized by bottom layer, by spectrum and, simultaneously, by spectrum and by bottom layer. We have also proved some results of recognizability of groups by bottom layer.

scholarly journals On a bottom layer in a group

2020 ◽  
Vol 100 (4) ◽  
pp. 136-142
Author(s):  
V.I. Senashov ◽  
◽  
I.A. Paraschuk ◽  
◽  
Keyword(s):  
Finite Elements ◽  
Finite Number ◽  
Finite Index ◽  
Finite Groups ◽  
Prime Order ◽  
Bottom Layer ◽  
Arbitrary Group ◽  
Locally Finite

We consider the problem of recognizing a group by its bottom layer. This problem is solved in the class of layer-finite groups. A group is layer-finite if it has a finite number of elements of every order. This concept was first introduced by S. N. Chernikov. It appeared in connection with the study of infinite locally finite p-groups in the case when the center of the group has a finite index. S. N. Chernikov described the structure of an arbitrary group in which there are only finite elements of each order and introduced the concept of layer-finite groups in 1948. Bottom layer of the group G is a set of its elements of prime order. If have information about the bottom layer of a group we can receive results about its recognizability by bottom layer. The paper presents the examples of groups that are recognizable, almost recognizable and unrecognizable by its bottom layer under additional conditions.

An Infinite Number of Laminagrams from a Finite Number of Radiographs

Radiology ◽  
1971 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Earl R. Miller ◽  
Edward M. MoCurry ◽  
Bernard Hruska
Keyword(s):  
Finite Number ◽  
Infinite Number

Some comments on positron–atom scattering at intermediate energy

1982 ◽  
Vol 60 (4) ◽  
pp. 558-564 ◽  
Author(s):  
F. W. Byron Jr.
Keyword(s):  
Finite Number ◽  
Cross Sections ◽  
Infinite Number ◽  
Intermediate Energy ◽  
Total Cross Sections ◽  
Type Approximation ◽  
Atom Scattering ◽  
Target States

A brief survey of available theoretical techniques is given for positron–atom scattering. The distinction between methods involving a finite number of target states and those with an infinite number of target states is emphasized. The situation regarding total cross sections is summarized, and a new, non-perturbative, eikonal-type approximation, based on the work of Wallace, is introduced.

scholarly journals Research of Register Pressure Aware Loop Unrolling Optimizations for Compiler

2018 ◽  
Vol 228 ◽  
pp. 03008
Author(s):  
Xuehua Liu ◽  
Liping Ding ◽  
Yanfeng Li ◽  
Guangxuan Chen ◽  
Jin Du
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Performance Degradation ◽  
Transformation Process ◽  
Fine Grained ◽  
Loop Unrolling ◽  
Average Improvement ◽  
Register Pressure ◽  
Linpack Benchmark ◽  
Loop Optimizations

Register pressure problem has been a known problem for compiler because of the mismatch between the infinite number of pseudo registers and the finite number of hard registers. Too heavy register pressure may results in register spilling and then leads to performance degradation. There are a lot of optimizations, especially loop optimizations suffer from register spilling in compiler. In order to fight register pressure and therefore improve the effectiveness of compiler, this research takes the register pressure into account to improve loop unrolling optimization during the transformation process. In addition, a register pressure aware transformation is able to reduce the performance overhead of some fine-grained randomization transformations which can be used to defend against ROP attacks. Experiments showed a peak improvement of about 3.6% and an average improvement of about 1% for SPEC CPU 2006 benchmarks and a peak improvement of about 3% and an average improvement of about 1% for the LINPACK benchmark.

On multilattice groups. II

1966 ◽  
Vol 62 (2) ◽  
pp. 149-164 ◽  
Author(s):  
D. B. Mcalister
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Positive Element ◽  
Necessary And Sufficient Conditions ◽  
Countable Number ◽  
Direct Sums ◽  
Lattice Group ◽  
Ordered Groups ◽  
Group A ◽  
Necessary And Sufficient

Conrad ((2)), has shown that any lattice group which obeys (C.F.) each strictly positive element exceeds at most a finite number of pairwise orthogonal elements may be constructed, from a family of simply ordered groups, by carrying out, alternately, the operations of forming finite direct sums and lexico extensions, at most a countable number of times. The main result of this paper, Theorem 3.1, gives necessary and sufficient conditions for a multilattice group, which obeys (ℋ*), to be isomorphic to a multilattice group which is constructed from a family of almost ordered groups, by carrying out, alternately, the operations of forming arbitrary direct sums and lexico extensions, any number of times; we call such a group a lexico sum of the almost ordered groups.

A definition of existence in terms of abstraction and disjunction

1957 ◽  
Vol 22 (4) ◽  
pp. 343-344
Author(s):  
Frederic B. Fitch
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Recursive Relation ◽  
Basic Logic ◽  
Class A ◽  
Definition Of ◽  
Image Position

Greater economy can be effected in the primitive rules for the system K of basic logic by defining the existence operator ‘E’ in terms of two-place abstraction and the disjunction operator ‘V’. This amounts to defining ‘E’ in terms of ‘ε’, ‘έ’, ‘o, ‘ό’, ‘W’ and ‘V’, since the first five of these six operators are used for defining two-place abstraction.We assume that the class Y of atomic U-expressions has only a single member ‘σ’. Similar methods can be used if Y had some other finite number of members, or even an infinite number of members provided that they are ordered into a sequence by a recursive relation represented in K. In order to define ‘E’ we begin by defining an operator ‘D’ such thatHere ‘a’ may be thought of as an existence operator that provides existence quantification over some finite class of entities denoted by a class A of U-expressions. In other words, suppose that ‘a’ is such that ‘ab’ is in K if and only if, for some ‘e’ in A, ‘be’ is in K. Then ‘Dab’ is in K if and only if, for some ‘e and ‘f’ in A, ‘be’ or ‘b(ef)’ is in K; and ‘a’, ‘Da’, ‘D(Da)’, and so on, can be regarded as existence operators that provide for existence quantification over successively wider and wider finite classes. In particular, if ‘a’ is ‘εσ’, then A would be the class Y having ‘σ’ as its only member, and we can define the unrestricted existence operator ‘E’ in such a way that ‘Eb’ is in K if and only if some one of ‘εσb’, ‘D(εσ)b’, ‘D(D(εσ))b’, and so on, is in K.

scholarly journals On the Reduction of Ferrers' Associated Legendre Function

1929 ◽  
Vol 1 (4) ◽  
pp. 241-243
Author(s):  
Hrishikesh Sircar
Keyword(s):  
Finite Number ◽  
Infinite Series ◽  
Infinite Number ◽  
Legendre Function ◽  
Legendre Functions ◽  
Associated Legendre Functions ◽  
Reduced Order ◽  
Zonal Harmonics ◽  
Integral Degree ◽  
Associated Legendre Function

Introduction. In the present paper a formula will be obtained to express a Ferrers' Associated Legendre Function of any integral degree and order as a sum of a finite number of Associated Legendre Functions of an order reduced by an even number. When the order is reduced by unity, an infinite series of the functions of reduced order is required. Thus a Ferrers' function can be expressed as the sum of a finite or infinite number of zonal harmonics according as the order of the function is even or odd.

scholarly journals Solution of the Word Problem for Certain Types of Groups I

1956 ◽  
Vol 3 (1) ◽  
pp. 45-54 ◽  
Author(s):  
J. L. Britton
Keyword(s):  
Finite Number ◽  
Word Problem ◽  
Infinite Number ◽  
Finite System ◽  
Defining Relations ◽  
Number Of Generators ◽  
Infinite Word ◽  
Formed Part ◽  
Free Product Of Groups ◽  
Product Of Groups

The main result of this series of papers is a theorem on the free product of groups (Theorem 1) which formed part of a doctoral thesis. This theorem has an immediate application to the word problem (Theorem 2). Usually the word problem refers to a finite system of generators and a finite number of defining relations, but in this context it is more natural to allow an infinite number of generators and defining relations. This (infinite) word problem is not solvable in general (Example 2).

Periodic forest whose largest clearings are of size 3

1970 ◽  
Vol 266 (1172) ◽  
pp. 113-121 ◽  
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Basic Theory

Miller has observed that there are a finite number of periodic forests whose largest clearings are of size 1 or 2, and an infinite number whose largest clearings are of size 4. In this note the basic theory of periodic forests is outlined, and the number of periodic forests whose largest clearings are of size 3 is examined. There are 12 such forests; their corresponding tessellations are sketched.

Mesoscopic Continuous and Discrete Channels for Quantum Information Transfer

2006 ◽  
Vol 13 (03) ◽  
pp. 273-280
Author(s):  
Ferdinando de Pasquale ◽  
Gian Luca Giorgi ◽  
Simone Paganelli
Keyword(s):  
Quantum Information ◽  
Finite Number ◽  
Infinite Number ◽  
Anderson Model ◽  
Weak Coupling ◽  
Information Transfer ◽  
Degrees Of Freedom ◽  
Quantum State Transfer ◽  
State Transfer ◽  
Discrete Channels

We study the possibility of realizing perfect quantum state transfer in mesoscopic devices. We discuss the case of the Fano-Anderson model extended to two impurities in a single excitation regime. For a channel with an infinite number of degrees of freedom, we obtain coherent behaviour in the case of strong coupling or in weak coupling off-resonance. For a finite number of degrees of freedom, coherent behaviour is associated to weak coupling and resonance conditions.

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