Regular Sequences of Symmetric Polynomials
... ABSTRACT - A set of n homogeneous polynomials in n variables is a regular sequence if the associated polynomial system has only the obvious solution (0; 0; . . . ; 0). Denote by pk (n) the power sum symmetric polynomial in n variables x1k x2k . . . xnk . The interpretation of the q-analogue of ...
... ABSTRACT - A set of n homogeneous polynomials in n variables is a regular sequence if the associated polynomial system has only the obvious solution (0; 0; . . . ; 0). Denote by pk (n) the power sum symmetric polynomial in n variables x1k x2k . . . xnk . The interpretation of the q-analogue of ...
A Traffic-Based Method of Detecting Dead IKE Peers
... When two peers communicate with IKE [2] and IPSec [3], the situation may arise in which connectivity between the two goes down unexpectedly. This situation can arise because of routing problems, one host rebooting, etc., and in such cases, there is often no way for IKE and IPSec to identify the loss ...
... When two peers communicate with IKE [2] and IPSec [3], the situation may arise in which connectivity between the two goes down unexpectedly. This situation can arise because of routing problems, one host rebooting, etc., and in such cases, there is often no way for IKE and IPSec to identify the loss ...
axioms
... set based upon another axiom set which we are willing to assume is consistent. • For example, we accept the validity of the axioms for the real numbers (or the real number line) even though we can not produce a concrete, real-world model (we only have a finite number of objects to manipulate). If we ...
... set based upon another axiom set which we are willing to assume is consistent. • For example, we accept the validity of the axioms for the real numbers (or the real number line) even though we can not produce a concrete, real-world model (we only have a finite number of objects to manipulate). If we ...
COBORDISM AND THE EULER NUMBER
... admits a vector field interior normal on the boundary and having at most one singular point, the index of this point being X. If we reverse the sense of the field at each point of N’, the index of the singularity changes to -X. (If n + 1 is even, this is true only because X = 0.) Hence if we use the ...
... admits a vector field interior normal on the boundary and having at most one singular point, the index of this point being X. If we reverse the sense of the field at each point of N’, the index of the singularity changes to -X. (If n + 1 is even, this is true only because X = 0.) Hence if we use the ...
Periodicity and Correlation Properties of d
... of ones minus the number of zeroes in one period of the sequence formed by adding S to the t-shift of T, bit by bit modulo 2. Recently Klapper and Goresky [12] the authors considered a slightly different notion of cross-correlation between sequences: the arithmetic cross-correlation (with shift t) o ...
... of ones minus the number of zeroes in one period of the sequence formed by adding S to the t-shift of T, bit by bit modulo 2. Recently Klapper and Goresky [12] the authors considered a slightly different notion of cross-correlation between sequences: the arithmetic cross-correlation (with shift t) o ...
Theory Behind RSA
... being able to find large primes quickly, whereas anyone given the product of two large primes “cannot” factor the number in a reasonable time. Even if we know e we cannot figure out d unless we know (n). To find (n), we need to factor n. While there is no proof that factorization is computatio ...
... being able to find large primes quickly, whereas anyone given the product of two large primes “cannot” factor the number in a reasonable time. Even if we know e we cannot figure out d unless we know (n). To find (n), we need to factor n. While there is no proof that factorization is computatio ...
Logical Omniscience As Infeasibility - boris
... that the agent is capable of performing modus ponens, and (2) says that it can recognize valid facts of the theory. Both postulates can be justified by the assumption that agents are rational reasoners. Working with normal modal logics yields the possibility of using the semantics of Kripke models, ...
... that the agent is capable of performing modus ponens, and (2) says that it can recognize valid facts of the theory. Both postulates can be justified by the assumption that agents are rational reasoners. Working with normal modal logics yields the possibility of using the semantics of Kripke models, ...
Transcendence of Various Infinite Series Applications of Baker’s Theorem and
... The formula shows that the values at even arguments of the Riemann zeta function have the property of being transcendental, which we define now. Definition 1.1. A complex number is said to be algebraic if it is the root of a polynomial with integer coefficients. Definition 1.2. A complex number is s ...
... The formula shows that the values at even arguments of the Riemann zeta function have the property of being transcendental, which we define now. Definition 1.1. A complex number is said to be algebraic if it is the root of a polynomial with integer coefficients. Definition 1.2. A complex number is s ...
Sequence entropy pairs and complexity pairs for a measure
... On the other hand, by Theorem 2.3 and [S], if (X, p, T) is measuretheoretical weakly mixing then (X, p, T) is seq-K. So (X, p, T) is measuretheoretical weakly mixing if and only if it is seq-K and a seq-K system is M-supe with X(2) B A2(X). We mention that M-supe does not imply seq-K since there is ...
... On the other hand, by Theorem 2.3 and [S], if (X, p, T) is measuretheoretical weakly mixing then (X, p, T) is seq-K. So (X, p, T) is measuretheoretical weakly mixing if and only if it is seq-K and a seq-K system is M-supe with X(2) B A2(X). We mention that M-supe does not imply seq-K since there is ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.