We compute the number of solutions of the equation Tr F t/ F s(f(x)+v. x)=b in F t 2N, where f denote a quadratic hermitian form on F t 2N, v∈ F t 2N and b∈ F s, and we deduce the number of hermitian matrices of order N and rank ρ. This number is well-known ...
A Formula for the Number of solutions of the Congruence αx~a+βy~b+γz~c≡0(modp~n) AFormulafortheNumberofsolutionsoftheCongruenceαx~a+βy~b+γz~c≡0(modp~n)HanQing(韩清)(Dept.ofMath.,SichuanUniv,Chengdu,Sichuan,6160...
Let xx ' ≡1(modn). The authors find an explicit formula for the number N(n) of solutions (k 1 ,k 2 ,k 3 ,k 4 ) of k 1 +k 2 ≡k 3 +k 4 (modn), k 1 ' +k 2 ' ≡k 3 ' +k 4 ' (modn) in the reduced system of residues. It is shown that N is a multiplic...
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Schinzel showed that for each xed k 8 1047 there are at least two solutions to (n )= (n + k). Using the same method and a computer search, Schinzel and A. Wakulicz extended the bound to all k 2 1058. Here we show that Schinzel's method can be used to further extend the ...
To solve the given equations and find the number of solutions, we will analyze each equation step by step.Equation 1:
How can the number of terms N be estimated if there are no closed form solutions available for the bounds of the derivatives of the density of the log-returns? We suggest solving the right-hand side of Inequality (3.8) numerically to find a bound for \(\Vert f^{(k+1)}\Vert _{\inf...
Length of prime implicants and number of solutions of random CNF formulae Summary: Consider a uniform distribution of $r$-CNF formulae (in Conjunctive Normal Form) with cn clauses, each with $r$ distinct literals, over a set of $... Y Boufkhad,O Dubois - 《Theoretical Computer Science》...
Btw, upload the Excel file instead of images so that other experts can also have a look at your file and tweak the formula or offer different solutions. Reply Show More ashishG1984 Copper Contributor to SergeiBaklanSep 06, 2019 SergeiBaklan Hello, Good Morning !!...
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