Table of Contents Details
...5.2 Structural equation in Riemannian manifold. . . . . . . . . . 263 5.5.3 Local form of Riemannian curvature tensor . . . . . . . . . . . 263 5.6 Integration on combinatorial manifolds . . . . . . . . . . . . .265 5.6.1 Determining H (n,m) . . . . . . . . . . . . . . . . . .265 5.6.2 Partition of unity . . . . . . . . . . . . . . . . . . . . . . 266 5.6.3 Integratio...

Full Text Search Details
...ions and curvatures on tensors orcombinatorial Riemannian manifolds, integrations and the generalization of Stokes’and Gauss’ theorem, and s... ...rvature tensor . . . . . . . . . . . . . . . . . . . . . . . . . 263§5.6 Integration on combinatorial manifolds. . . . . . . . . . . . . . . . . . .... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 5.6.3 Integration on combinatorial manifold . . . . . . . . . . . . . . . . . . .... .... n→∞The following result, called Lebesgue lemma, is a useful result in metric spaces.Theorem 3.1.3(Lebesgue ... ...n λ is contained in one of member of {Vα|α ∈ Π}. The numberλ is called the Lebesgue number. Proof The proof is by contradiction. If there no such... ...besgue number. Proof The proof is by contradiction. If there no such Lebesgue number λ,choosing numbers ǫ1, ǫ2, · · · with lim ǫn = 0, we co... ...ct metric space. Choose an integern so large that 1/n is less than the Lebesgue number of this cover. We divide theinterval I into these closed... ...ir topological and differential behaviors.Problem 3.6.2 Define integrations and then generalize Stokes, Gauss,... ... ... 11 combinatorial field 420Higgs field 402 Lebesgue Lemma 96Higgs particle 402 Lie algebra 318homo...

Full Text Search Details
... instant α-readingsMULTI-SENSORDATA FUSION  Data fusion: process of integration of multiple data and knowledge representing the same real-... ...space. Lexicographic ordering. Hybrid space is a cartesian space. Lebesgue measure. Combining logic with probability (Nillson). Motion ... ... instant α-readingsDATA MINING INBIOINFORMATICS  Data integration, data interpretation.  Bioinformatics: umbrella term for t...

Full Text Search Details
...ments of a set or between criteriain real life problems. Actually, the concept is an enlargement of the Lebesgue integral anda non-additive ... ...hasmore complicated structure due to the lack of additivity in contrast to the additive integralssuch as Lebesgue integral, use of a fuzzy measu... ...d PreferenceRanking Organization Method for Enrichment Evaluations (PROMETHEE II) are suggested as aneffective integration in multi-criteria decision ... ...cision making for selecting appropriate drug product under specific conditionsusing Neutrosophic theory by the integration of the BWM, MABAC and PROME... ...02 289A hybrid decision making framework has been designed and built on the integration by extendingBWM, MABAC, PRO... ...t: The purpose of this article is to study the neutrosophic integrals by parts, all cases in whichwe can apply integration by parts are discussed, inc... ...hic complex numbers, the general exponential form of a neutrosophic complex, andthe neutrosophic integrals and integration methods [7-14-24]. On the ...

Full Text Search Details
...ed of the Jordan-Brans- Dicke scalar. We will see soon why the integration constant Vo plays the role of the ”cosmological cons... ...q-(26) is that the observed vacuum energy density is minus the constant of integration Vo corresponding to the potential density V (φ) = 12H ... ...ctions, with and without a cosmological constant [123], and based on a new integration measure by recurring to auxiliary scalar fields [115], that one ... ...isymmetric part of the field strength. This requires closing off the integration countour by a semi-circle that starts at S = +∞, goes all the ... ... then used the Bianchi identity for the antisymmetric componentF[MN]. The integration by parts permits us to go from a C-space domain integral, repre... ...his produces that the random lagrangian flow preserves the Lebesgue measure on R3, as it can be easily verified. This ...

Full Text Search Details
...4, 2012 77a  1,..., v ; q  1,..., h ; l  1,..., kStep 3: Horizontal integration is done using DBBAO and by ... ...g DSmT on the evaluatedcharacteristic matrix to get the dynamic mass of all the failure modes.Step 4: Vertical integration of the dynamic masses of al... ... Step 2 Collect decision makers views on failure modes Step 3 Carry out horizontal integration applying DSmT ... ...g.3. Steering Gear system with failure modesDynamic masses of all the failure modes are obtained by horizontal integration using DSmT andDBBAO. These ... ...plications (based on neutrosophic sets)for decision making algorithm. In future, we will discuss the following integration of the related topics;_____... ...a probability space (Ω, A, P ) = ([0, 1], A, m) where A is a Borel field on [0, 1] and m is the usual Lebesgue measure. Let H˜ :...

Full Text Search Details
...Wang, F. Smarandache, Y. Q. Zhang, and R.[2] H. J. S. Smith. On the integration of discontinuous Sunderraman. Single valued neutrosop... ... 0 2 ˜ ˜ ˜ ˜ . . .Lebesgue measure. Let H := (HT , HI , HF ) be a neutrosophic 1 ...

Full Text Search Details
...2 (5) As a consequence of this lemma, we obtain from (6) and a simple integration Corollary 1. For x > 1 we have: ... ...1L. Lander 2.12 NE.S. Langford 3.20 N. Nair 4.11A. Lebesgue 2.8 I. Newton 3.17G. von Leibniz 5....

Full Text Search Details
...m which we know as science (in fact it only exists as anideal, we only know of the existence of the sciences, with no integration ofthem), one of the ... ...not been solved yet. Some of the ideas being proposed is the use of biofuels,which itself is not sustainable with due integration of Humankind, and th... ... quantization con-dition with I pidqi = ni h , ¯ Nwhere the integration is over the previous... ...×dW 0 ∂x 0The integral in the first term of eq. (201) is an isotopic integral of a usualRiemann-Lebesgue integral, while the sec... ...vices would be nonvolatility, increaseddata processing speed, decreased electrical power consumption, andincreased integration densities comp...

Full Text Search Details
... i j=1Notice that pi(x) is put inside the integration, so as to deal with possiblesingularities, when ... ... the singletons in 2Θ) until the total indecision Θ (s = 0). λXallows the integration of the lack of knowledge on one of the elements X ... ...), max(yi , yi )] (9.26) i=1 The measure of Lebesgue gives the cardinal of interval: ... ...nteresting or not. Assigning gbba to the paradoxical case allows for the integrationof the opinions of other experts even if they are conflicti... ... T. Garvey, Evidential reasoning: an implementation for multisen- sor integration, Technical Note 307, Artificial Intelligence Center, Inter... ...ance, T. Garvey, Evidential reasoning: an implementation for multisensor integration, Technical Note 307, Artificial Intelligence Center, Inter...

Full Text Search Details
...ets Syst, 1987, Volume 24, pp. 301-317.23. Dubois, D., Prade, H.; Towards fuzzy differential calculus part 2: Integration on fuzzy intervals, Fuzzy S... ...on and Engi- neering, 9(3), 299-324. [7] Biswas, S., Moi, S., & Sarkar, S. P. (2021). Neutrosophic Riemann integration and its properties. Soft ... ... theory to a variety of fields, including the smoothness of functions, game theory,operation research, Riemann integration, and elsewhere [1,2]. Appli... ... 9Step 6 : Combine the opinions of all experts in one integration matrix and measur... ...ce constrained programming; Trust mea-sure;—————————————————————————————————————————-1. Introduction Nowadays, integration of the effects of marketing... ... For a real life problem when sufficient information is given about the measurement of π, it maybe treated as Lebesgue measure. More generally, the t... ...sT r {A} = (1 − η)T r {A} + ηT r {A} , 0 < η < 1. Let ξˆ = ([m, n][p, q]), p ≤ m ≤ n ≤ q be a rough variable. Lebesgue measure is considered for thet...

Full Text Search Details
... as smoothness of functions, game theory, operation research, Riemann integration, Perron integration, and probability. Re- cently so... ... 2 ˜ ˜ ˜ ˜ . . . Lebesgue measure. Let H := (HT , HI , HF ) be a neutrosophic 1 ... ...formation and inconsistent information, could be handled well with the integration of multi-stage fault template data and the neutrosophic set... ...e will discuss mutually isomorphic: (the tables are omitted). the integration of the related topics, such as the Theorem 13. Let (N, ∗) be ...