Matches in SemOpenAlex for { <https://semopenalex.org/work/W3048137709> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W3048137709 endingPage "96" @default.
- W3048137709 startingPage "79" @default.
- W3048137709 abstract "The main purpose of this article is to provide an exact theory of the dynamic programming on a sufficiently general basis. Let $M$ be a compact topological Hausdorff's space, let $tilde {T}^M$ be the set of all continuous transformations of the space $M$ into itself. Suppose such a topology is introduced on $tilde {T}^M$ that $tilde {T}^M$ is Haousdorff's space and that the transformation $phi(x,y)=y(x)$ of the product $M otimes tilde {T}^M$ into $M$ is continuous with respect to Tichonoff's topology on $M otimes tilde {T}^M$. Suppose $tilde {T}^M$ is a compact subspace of $tilde {T}^M$ and $Cal M = M otimes T^M otimes ldots otimes T^M otimes ldots$. We define the transformations $P, N$ and the set $Cal M^{(x_o)}$ as followe: For each $X=(x_0, y_0, y_1, ldots)in Cal M$ it is: $PX=(y_0(x_0),y_1,ldots), NX=x_0, Cal M^{(x_0)}={X; X in Cal M, NX= x_0}$. Suppose $Psi$ is a continuous function defined on $Cal M$ and $f(x_0)= max_{xin Cal M^{(x_0)}} Psi(X)$. The dynamic programming problem can now be formulated as follows: For all $xin M$ find the element (or elements) $bar{X}in Cal M^{(x)}$ for which $Psi(bar{X})=f(x)$. Existence and uniqueness of the solution of this problem is proved and the method of succesive approximations is used to solve it in case when $Psi(X)-Psi(PX)=Theta(x_0, y_0)$. Further the case $Psi(X)=sum^infty_{i=0}Theta_i(x_i, y_i)$ is considered and one minor example is solved." @default.
- W3048137709 created "2020-08-13" @default.
- W3048137709 creator A5007875599 @default.
- W3048137709 creator A5062179552 @default.
- W3048137709 date "1970-01-01" @default.
- W3048137709 modified "2023-09-26" @default.
- W3048137709 title "One generalization of the dynamic programming problem" @default.
- W3048137709 doi "https://doi.org/10.21136/am.1970.103272" @default.
- W3048137709 hasPublicationYear "1970" @default.
- W3048137709 type Work @default.
- W3048137709 sameAs 3048137709 @default.
- W3048137709 citedByCount "1" @default.
- W3048137709 crossrefType "journal-article" @default.
- W3048137709 hasAuthorship W3048137709A5007875599 @default.
- W3048137709 hasAuthorship W3048137709A5062179552 @default.
- W3048137709 hasBestOaLocation W30481377091 @default.
- W3048137709 hasConcept C114614502 @default.
- W3048137709 hasConcept C118615104 @default.
- W3048137709 hasConcept C134306372 @default.
- W3048137709 hasConcept C138885662 @default.
- W3048137709 hasConcept C142730499 @default.
- W3048137709 hasConcept C18648836 @default.
- W3048137709 hasConcept C191399826 @default.
- W3048137709 hasConcept C2524010 @default.
- W3048137709 hasConcept C2777021972 @default.
- W3048137709 hasConcept C2778572836 @default.
- W3048137709 hasConcept C32834561 @default.
- W3048137709 hasConcept C33923547 @default.
- W3048137709 hasConcept C41895202 @default.
- W3048137709 hasConcept C81332173 @default.
- W3048137709 hasConcept C90673727 @default.
- W3048137709 hasConceptScore W3048137709C114614502 @default.
- W3048137709 hasConceptScore W3048137709C118615104 @default.
- W3048137709 hasConceptScore W3048137709C134306372 @default.
- W3048137709 hasConceptScore W3048137709C138885662 @default.
- W3048137709 hasConceptScore W3048137709C142730499 @default.
- W3048137709 hasConceptScore W3048137709C18648836 @default.
- W3048137709 hasConceptScore W3048137709C191399826 @default.
- W3048137709 hasConceptScore W3048137709C2524010 @default.
- W3048137709 hasConceptScore W3048137709C2777021972 @default.
- W3048137709 hasConceptScore W3048137709C2778572836 @default.
- W3048137709 hasConceptScore W3048137709C32834561 @default.
- W3048137709 hasConceptScore W3048137709C33923547 @default.
- W3048137709 hasConceptScore W3048137709C41895202 @default.
- W3048137709 hasConceptScore W3048137709C81332173 @default.
- W3048137709 hasConceptScore W3048137709C90673727 @default.
- W3048137709 hasIssue "2" @default.
- W3048137709 hasLocation W30481377091 @default.
- W3048137709 hasOpenAccess W3048137709 @default.
- W3048137709 hasPrimaryLocation W30481377091 @default.
- W3048137709 hasRelatedWork W1968542100 @default.
- W3048137709 hasRelatedWork W1968801166 @default.
- W3048137709 hasRelatedWork W197493210 @default.
- W3048137709 hasRelatedWork W2014270013 @default.
- W3048137709 hasRelatedWork W2020342936 @default.
- W3048137709 hasRelatedWork W2086648911 @default.
- W3048137709 hasRelatedWork W2950667316 @default.
- W3048137709 hasRelatedWork W3135427014 @default.
- W3048137709 hasRelatedWork W4253304777 @default.
- W3048137709 hasRelatedWork W4312815326 @default.
- W3048137709 hasVolume "15" @default.
- W3048137709 isParatext "false" @default.
- W3048137709 isRetracted "false" @default.
- W3048137709 magId "3048137709" @default.
- W3048137709 workType "article" @default.