On the monotonicity of the number of positive entries in nonnegative five-element matrix powers

2021 ◽  
Vol 14 (4) ◽  
pp. 703-721
Author(s):  
Matthew Rodriguez Galvan ◽  
Vadim Ponomarenko ◽  
John Salvadore Sabio
Keyword(s):  
Element Matrix

scholarly journals 3-D Synthetic Aperture High Volume Rate Tensor Velocity Imaging Using 1024 Element Matrix Probe

2020 ◽  
Author(s):  
Fatemeh Makouei ◽  
Babak Mohammadzadeh Asl ◽  
Lasse Thurmann Jorgensen ◽  
Borislav Gueorguiev Tomov ◽  
Matthias Bo Stuart ◽  
...  
Keyword(s):  
High Volume ◽  
Synthetic Aperture ◽  
Volume Rate ◽  
Velocity Imaging ◽  
Element Matrix

GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

2018 ◽  
Vol 37 (7) ◽  
pp. 443-454 ◽  
Author(s):  
J. S. Mueller‐Roemer ◽  
A. Stork
Keyword(s):  
Finite Element ◽  
Matrix Assembly ◽  
Element Matrix

scholarly journals On the Asymptotic Spectrum of Finite Element Matrix Sequences

2007 ◽  
Vol 45 (2) ◽  
pp. 746-769 ◽  
Author(s):  
Bernhard Beckermann ◽  
Stefano Serra‐Capizzano
Keyword(s):  
Finite Element ◽  
Asymptotic Spectrum ◽  
Element Matrix

Explicit Triangular Bending Element Matrix

1974 ◽  
Vol 100 (7) ◽  
pp. 1459-1472
Author(s):  
William S. Doyle ◽  
Robert L. Harrison
Keyword(s):  
Element Matrix

Many-valued logics, philosophical issues in

2018 ◽  
Author(s):  
Lloyd Humberstone
Keyword(s):  
Free Action ◽  
Borderline Case ◽  
Main Body ◽  
Plane Crash ◽  
Sentential Logic ◽  
The Status ◽  
The Individual ◽  
Element Matrix ◽  
Excluded Middle ◽  
Truth Tables

The first philosophically-motivated use of many-valued truth tables arose with Jan Łukasiewicz in the 1920s. What exercised Łukasiewicz was a worry that the principle of bivalence, ‘every statement is either true or false’, involves an undesirable commitment to fatalism. Should not statements about the future whose eventual truth or falsity depends on the actions of free agents be given some third status – ‘indeterminate’, say – as opposed to being (now) regarded as determinately true or determinately false? To implement this idea in the context of the language of sentential logic (with conjunction, disjunction, implication and negation), we need to show – if the usual style of treatment of such connectives in a bivalent setting is to be followed – how the status of a compound formula is determined by the status of its components. Łukasiewicz’s decision as to how the appropriate three-valued truth-functions should look is recorded in truth tables in which (determinate) truth and falsity are represented by ‘1’ and ‘3’ respectively, with ‘2’ for indeterminacy (see tables in the main body of the entry). Consider the formula A∨B (‘A or B’), for example, when A has the value 2 and B has the value 1. The value of A∨B is 1, reasonably enough, since if A’s eventual truth or falsity depends on how people freely act, but B is determinately true already, then A∨B is already true independently of such free action. There are no constraints as to which values may be assigned to propositional variables. The law of excluded middle is invalidated in the case of indeterminacy: if p is assigned the value 2, then p∨ ¬p also has the value 2. This reflects Łukasiewicz’s idea that such disjunctions as ‘Either I shall die in a plane crash on January 1, 2030 or I shall not die in a plane crash on January 1, 2030’ should not be counted as logical truths, on pain of incurring the fatalistic commitments already alluded to. Together with the choice of designated elements (which play the role in determining validity played by truth in the bivalent setting), Łukasiewicz’s tables constitute a (logical) matrix. An alternative three-element matrix, the 1-Kleene matrix, involves putting 2→2=2, leaving everything else unchanged. And a third such matrix, the 1,2-Kleene matrix, differs from this in taking as designated the set of values {1,2} rather than {1}. The 1-Kleene matrix has been proposed for the semantics of vagueness. In the case of a sentence applying a vague predicate, such as ‘young’, to an individual, the idea is that if the individual is a borderline case of the predicate (not definitely young, and not definitely not young, to use our example) then the value 2 is appropriate, while 1 and 3 are reserved for definite truths and falsehoods, respectively. Łukasiewicz also explored, as a technical curiosity, n-valued tables constructed on the same model, for higher values of n, as well as certain infinitely many-valued tables. Variations on this theme have included acknowledging as many values as there are real numbers, with similar applications to vagueness and approximation in mind.

Disassembly Analysis Based on Entropy and Extension Theory

2012 ◽  
Vol 569 ◽  
pp. 472-476
Author(s):  
Na Zhao ◽  
Rui Mu ◽  
Wei Huang ◽  
Wen Guang Lin
Keyword(s):  
Product Design ◽  
Evaluation Model ◽  
Evaluation Process ◽  
Extension Theory ◽  
Weight Matrix ◽  
Element Analysis ◽  
Matter Element Analysis ◽  
Element Matrix ◽  
Index Weight

In view of the fuzziness and uncertainty characteristics of the index and evaluation incompatibility in the disassembly evaluation process, the disassembly evaluation model of fuzzy matter-element analysis based on entropy was proposed. Firstly, the fuzzy matter-element matrix and weight matrix was established, based on the analysis of the factors having influences on disassemblability. Then the dependent degree of each scheme was calculated to rank disassemblability of the product design schemes. Additionally, the index weight was determined by the method of entropy, which can effectively avoid interference of subjective factors in the process of weight determination. Finally, an example of disassemblability evaluation was given to show the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document