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Microlocal analysis of scattering data for nested conormal potentials
[article]

2011
*
arXiv
*
pre-print

We utilize the microlocal analysis

arXiv:1103.6015v2
fatcat:cakifxo7o5e6fjtrjjes4ujgva
*of*the wave operator =∂_t^2 - _x and multiplication by a*nested**conormal*distribution in order to study their action on spaces*of**conormal*-like distributions. ... Working in the time domain, we show that the location*of*the singularities and the principal symbol*of*a potential that is*conormal*to*nested*submanifolds S_2 ⊂ S_1 ⊂R^n, for n ≥ 3, can be recovered from ... A portion*of*this work was supported by NSF grant DMS-0853892. ...##
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Microlocal analysis of scattering data for nested conormal potentials

2012
*
Journal of Functional Analysis
*

We utilize the microlocal analysis

doi:10.1016/j.jfa.2011.12.013
fatcat:rwbjwahplzfupndhwpqhhb6fre
*of*the wave operator = ∂ 2*t*− x and multiplication by a*nested**conormal*distribution in order to study their action on spaces*of**conormal*-like distributions. Crown ... Working in the time domain, we show that the location*of*the singularities and the principal symbol*of*a potential that is*conormal*to*nested*submanifolds S 2 ⊂ S 1 ⊂ R n , for n 3, can be recovered from ... A portion*of*this work was supported by NSF grant DMS-0853892. ...##
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Microlocal Analysis of Scattering Data for Nested Conormal Potentials
[chapter]

2012
*
Microlocal Methods in Mathematical Physics and Global Analysis
*

This work is a fairly straightforward generalization

doi:10.1007/978-3-0348-0466-0_20
fatcat:p5o4euv7avalpifewb6qkrjbwu
*of*the theory*of**nested**conormal*distributions. ... the previous lemma for*nested**conormal*distributions. ...##
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Operations with Nested Named Sets as a Tool forArtificial Intelligence

2022
*
Big Data and Cognitive Computing
*

Computing tools

doi:10.3390/bdcc6020037
fatcat:5ht3y4o5szd2bcmqrwfysalmfu
*of*AI include*nested*levels*of*parentheses in arithmetical expressions; different types*of*recursion;*nesting**of*several levels*of*subroutines;*nesting*in recursive calls; multilevel*nesting*... in information hiding; a variety*of**nested*data structures, such as records, objects, and classes; and*nested*blocks*of*imperative source code, such as*nested*repeat-until clauses, while clauses, if clauses ... Conflicts*of*Interest: The author declares no conflict*of*interest. ...##
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Ordinal Sums of De Morgan Triples

2018
*
TEMA
*

In this paper we consider the ordinal sum

doi:10.5540/tema.2018.019.02.181
fatcat:im5ttkekezcnvcrntuwpkuuqra
*of*the summands (a_i, b_i, T_i) ((a_i, b_i, S_i)), where (T_i)_{i\in I}$ $((S_i)_{i\in I}) are a family*of**t*-(co)norms and $(]a_i, b_i[)_{i\in I}$ a family*of*... In addition, we prove if (T_i, S_i, N_i) is a De Morgan triple satisfy some specific conditions, then (*T*, S, N) is a semi De Morgan triple. ... using*t*-norms and*t*-*conorms*theory. ...##
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Page 5969 of Mathematical Reviews Vol. , Issue 97J
[page]

1997
*
Mathematical Reviews
*

., there are more than 50 graphs

*of*different*t*-norms and*t*-*conorms*. ... It explains the basic notions*of*fuzzy set theory, such as fuzzy sets, a-levels,*t*-norms,*t*-*conorms*, fuzzy real numbers, fuzzy logic, and the relationship between fuzzy logic and proba- bility (fuzzy sets ...##
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On data fusion in information retrieval using different aggregation operators

2011
*
Web Intelligence and Agent Systems
*

This paper is concerned with the problem

doi:10.3233/wia-2011-0204
fatcat:cqrkwjdbfzewtp6ye3dgkklleu
*of*unsupervised rank aggregation in the context*of*metasearch in information retrieval. ... In this paper we investigate whether aggregation operators defined in the fields*of*multi-sensor fusion and multicriteria decision making are*of*interest for metasearch problems or not. ... Then, departing from a*t*-norm*T*, we can define its related triangular*conorm**T** (*t*-*conorm*) as follows:*T** (a, b) = 1 −*T*(1 − a, 1 − b) (6) Similarly to*t*-norms,*t*-*conorms*allow one to extend the disjunction ...##
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Conormal Spaces and Whitney Stratifications
[article]

2021
*
arXiv
*
pre-print

The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms

arXiv:2106.14555v1
fatcat:dek66tqpmbba5b4pgtrkqxpdau
*of**conormal*spaces and maps, and (b) a new interpretation*of*this*conormal*... We show that this algorithm improves upon the existing state*of*the art by several orders*of*magnitude, even for relatively small input varieties. ... VN is grateful to Mark Goresky and Robert MacPherson for several valuable discussions on the local geometry*of*singular spaces; his work was supported by EPSRC grant EP/R018472/1 and by DSTL grant D015 ...##
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S-Fuzzy Left H-Ideal Of Hemirings

2007
*
Zenodo
*

on hemirings are discussed.The notion

doi:10.5281/zenodo.1331666
fatcat:ghubs22cx5gonntn62kvogmbya
*of*direct product and S-product are introduced and some properties*of*the direct product and S-product*of*S-fuzzy left h-ideal*of*hemiring are also discussed. ... collection*of*left h-ideals*of*a hemiring, S-fuzzy left h-ideal*of*hemirings are established.The notion*of*a finite-valued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuzzy relations ... Proof: The proof is obtained dually by using the notion*of**t*-*conorm*S instead*of**t*-norm*T*in [9] . ...##
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Generalized and Customizable Sets inR

2009
*
Journal of Statistical Software
*

Note that the drastic

doi:10.18637/jss.v031.i02
fatcat:hqx56bfuyjdbjmjh5uzppyexky
*t*-norm and*t*-*conorm*are the smallest*t*-norm and largest*t*-*conorm*, respectively. ... "Zadeh" Zadeh's logic with*T*= min and S = max. Note that the minimum*t*-norm, also known as the Gödel*t*-norm, is the pointwise largest*t*-norm, and that the maximum*t*-*conorm*is the smallest*t*-*conorm*. ...##
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Page 4175 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

The right-hand side can be expressed as a Mellin transform o> exp(—tz) exp(

*t*{)dt. Put s =exp*t*, ds/s =dt. ... ere is 4175 58G Partial differential equations on manifolds; differential operators a*nested*sequence*of*normal subgroups --- Gn) C Gn C--- CG satisfying [G : G,,] finite and (),, G,, trivial. ...##
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A monotonic optimization approach for solving strictly quasiconvex multiobjective programming problems

2020
*
Journal of Intelligent & Fuzzy Systems
*

After the algorithm is terminated, with any given tolerance, we obtain an approximation

doi:10.3233/jifs-179690
fatcat:kwn5qrao6bdrph64e5zbg242te
*of*the weakly efficient solution set, that contains the whole weakly efficient solution set*of*the problem. ... Some computational experiments are reported to show the accuracy and efficiency*of*the proposed algorithm. ... Therefore, the compact*conormal*set Y can be approximated by a family*of*copolyblocks. Specifically, a*nested*sequence*of*copolyblocks is generated that outer-approximates the outcome set Y , i.e. ...##
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Estimates for singular radon transforms and pseudodifferential operators with singular symbols

1990
*
Journal of Functional Analysis
*

The Schwart;, kernel

doi:10.1016/0022-1236(90)90011-9
fatcat:dae3lagubvgktefdiyzubqqnx4
*of*R is KR(trX,S,y)=6(*t*-s+S(*t*,x,y))K(*t*,x,x-y). (2.18) Since 6( ) is a*conormal*distribution for the origin on [w', and a Calderon-Zygmunl kernel is*conormal*for the origin in BB", ... Let S2 G S, z X be*nested*manifolds with dim X= n and S,, SZ*of*~odimensions d,, dr + d2 in X, respectively. ...##
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Page 3308 of Mathematical Reviews Vol. , Issue 89F
[page]

1989
*
Mathematical Reviews
*

A

*nested*sequence (1) F!} c 92 c---c D3 c ---*of*principal fiber spaces can be considered over M,. A*nested*sequence 7(M,,) C*T*? ... (M,) C --» C*T*°(M,) C ---*of**nested*tangent bundles can be interpreted as a sequence*of**nested*adjoined fiber spaces (2) M! c---c M2 c---c Mjc.---. ...##
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(DS)-WEAK COMMUTATIVITY CONDITION AND COMMON FIXED POINT IN INTUITIONISTIC MENGER SPACES

2011
*
The Pure and Applied Mathematics
*

The aim

doi:10.7468/jksmeb.2011.18.3.201
fatcat:fj6tshmxsfb2pgruz7vmcovrwm
*of*this paper is to define a new commutativity condition for a pair*of*self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility*of*mappings in the settings*of*intuitionistic ... We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity*of*any mapping. ...*t*-*conorm*. ...
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