Nested summation symbols

Applications of Nested Summation Symbols to Quantum Chemistry Formalism and Programming Teehniques... 

Consequently, here are studied under the formulation of the Nested Summation Symbols (NSS s) symbolism some Quantum Chemical problems and topics. 

APPLICATIONS OF NESTED SUMMATION SYMBOLS TO QUANTUM CHEMISTRY... 

APPLICATIONS OF NESTED SUMMATION SYMBOLS TO QUANTUM CHEMISTRY D(j k) = Det I. ... 

Applications of nested summation symbols to Quantum Chemistry formalism and programming techniques R. Carbo and E. Besalu... 

With respect to tiie symbol E(k=0,N), let us use from now on a general expression like E(k=r,s) as a sequence of sums and borrowing a programming terminology let us call it a nested summation symbol. 

Still a more general nested summation symbol can be defined and written as E(k=r,s,d), where the vector d contains all the arbitrary increments associated to the progress of each nested sum index. 

It has also to be taken into account that a product of two nested summation symbols is another summation symbol. That is En(i)E (j)=E + (k), where the vector k is constructed by the direct sum ksi j. The rest of the nested sum constituent vectors are constructed in the same way. 

Nested summation symbols applications have been deeply studied elsewhere [45b]. 

Nested summation symbolism is very convenient for practical purposes, because successive generation of k vector elements can be programmed in a general way imder any high level language, using a unique do or for loop irrespective of the number of sums, or binomial expressions of type (3.4) entering the product (3.5). 

Nested Summation Symbols are ideal constructs for programming in a suitable hardware environment, for example using transputer boards [51] or any computing device with various CPU runnixig in parallel [62]. All operations attached to each vector k can be run in a separate CPU. Counting the times this can be done in... 

Applications of Nested Summation Symbols and Logical Eunctions Pedagogical Artificial Intelligence Devices for Eormulae Writing, Sequential Programming and Automatic Parallel Implementation. 

Besalu, E. Carb6, R. Applications of Nested Summation Symbols to Quantum Chemistry Formalism and Programming Techniques In Strategies and Applications in Quantum Chemistry from Astrophysics to Molecular Engineering An Hommage... 

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