Sentence examples for related sums from inspiring English sources

Some related results for q-Euler type sums and related sums (e.g. q-L-function and q-multiple zeta values) may be seen in the works of [17 37] and the references therein.

In Section 3.2 we discuss closed forms for related sums in two dimensions.

Some authors had studied the properties of S 1 ( d, c ) and related sums and obtained some interesting results, see [4 8] and [9].

Regarding the properties of S 1 ( d, c ) and related sums, some authors studied them and obtained many interesting results; see [4 7] and [8].

Our main result is the following trace formulas of the type in [2] relating (sum |lambda _j|^{n}) (for (nin frac{1}{2}{N}}hbb {N}})) to an expression involving the potential V. (Trace formulas) Let (Gamma ) be a star graph with edges ({e_j}, 1le jle n).

Two key differences are that the virial theorem relates summed rather than individual averages to each other, and it does not connect them to the temperature T. Another difference is that traditional derivations of the virial theorem use averages over time, whereas those of the equipartition theorem use averages over phase space.

In [16], Simsek defined a new sum related to the sums s 5 ( h, k ) as follows: Let h and k be integers with ( h, k ) = 1 Y ( h, k ) = 4 k ∑ j = 1 k − 1 ( − 1 ) j + [ h j k ] ( ( j k ) ).

The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes.

Since sums of spatiotemporally related objects are sums of concrete objects, and sums of concrete objects are concrete objects, Lewisian possible worlds are concrete objects.[25], [26] Another theory of possible worlds has been developed by David Armstrong.

Also, sports factors are characteristically related to SUM solely among urban girls, while the highest SUM is found in those girls who participate in sports for a prolonged period while being less successful.

Peter Scheifinger, president of an organization of Austrian architects and related professionals, summed up her importance in an Austrian daily newspaper, Der Standard: "With her concern for social welfare and her unyielding anti-fascism, she erected socially significant road signs for the Republic of Austria that extended beyond her artistic field of endeavor".