scholarly journals NeutroAlgebra is a Generalization of Partial Algebra

2020 ◽  
pp. 08-17
Author(s):  
Florentin Smarandache ◽  
Keyword(s):  
Partial Algebra ◽  
The Other ◽  
Partial Operation ◽  
Whole Space ◽  
Partial Algebras ◽  
Concept Attribute

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).

scholarly journals Unsolid and fluid strong varieties of partial algebras

2006 ◽  
Vol 2006 ◽  
pp. 1-19
Author(s):  
S. Busaman ◽  
K. Denecke
Keyword(s):  
Partial Algebra ◽  
The Other ◽  
Turing Machines ◽  
Left Hand ◽  
Recursive Functions ◽  
Right Hand ◽  
Algebraic Description ◽  
Partial Recursive Functions ◽  
Partial Algebras ◽  
The Right

A partial algebra𝒜=(A;(fiA)i∈I)consists of a setAand an indexed set(fiA)i∈Iof partial operationsfiA:Ani⊸→A. Partial operations occur in the algebraic description of partial recursive functions and Turing machines. A pair of termsp≈qover the partial algebra𝒜is said to be a strong identity in𝒜if the right-hand side is defined whenever the left-hand side is defined and vice versa, and both are equal. A strong identityp≈qis called a strong hyperidentity if when the operation symbols occurring inpandqare replaced by terms of the same arity, the identity which arises is satisfied as a strong identity. If every strong identity in a strong variety of partial algebras is satisfied as a strong hyperidentity, the strong variety is called solid. In this paper, we consider the other extreme, the case when the set of all strong identities of a strong variety of partial algebras is invariant only under the identical replacement of operation symbols by terms. This leads to the concepts of unsolid and fluid varieties and some generalizations.

III. On the influence of coal-dust in colliery explosions

1876 ◽  
Vol 24 (164-170) ◽  
pp. 354-372 ◽  
Keyword(s):  
Coal Dust ◽  
Coal Mines ◽  
The Other ◽  
Mean Annual Temperature ◽  
Whole Space ◽  
The Mean ◽  
As If

In coal-mines in which the temperature of the workings is considerably higher than the mean annual temperature at the surface, there is usually a layer of rubbish on the floor of the roadways and air-ways, which consists, in some places, almost entirely of dry coal-dust, and in others of coal-dust mixed with small pieces of coal and stone. If it could be shown, therefore, that a mixture of air and coal-dust is inflammable at ordinary pressure and temperature, there would be no difficulty in accounting for the extent and violence of many explosions which have occurred in mines in which no large accumulations of firedamp were known to exist; for it is only necessary to suppose that a sudden gust of wind (originated, for example, by the explosion of a small accumulation of firedamp) had swept through the adjoining galleries, raising a cloud of dust into the air, and then all the other phenomena would follow in regular order. The flame of the originally inflammable mixture would pass directly into the newly formed one, expanding its volume; the disturbance would be propagated over an ever widening area, until that area might possibly become coextensive with the workings themselves; and the consequences would be the same as if the whole space had been filled with an inflammable mixture before the disturbance began.

scholarly journals Reflection and Diffraction of Atomic de Broglie Waves by Evanescent Laser Waves - Bare-state Method

1996 ◽  
Vol 49 (4) ◽  
pp. 765 ◽  
Author(s):  
Xiao-Ping Feng ◽  
NS Witte ◽  
Lloyd CL Hollenberg ◽  
Geoffrey I Opat
Keyword(s):  
Differential Equations ◽  
Laplace Transformation ◽  
The Other ◽  
Bare State ◽  
Coupled Differential Equations ◽  
Born Series ◽  
De Broglie Waves ◽  
Whole Space ◽  
State Method ◽  
Dressed State

We present two results in an investigation of reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both results use the bare-state rather than dressed-state picture. One is based on the Born series, whereas the other is based on the Laplace transformation of the coupled differential equations. The two solutions yield the same theoretical expressions for reflected and diffracted atomic waves in the whole space, including the interaction and the asymptotic regions.

Self-Adaptive QoS-Aware Web Service Discovery Using Ontology Approach

Web Services ◽  
2019 ◽  
pp. 822-841 ◽  
Author(s):  
Nwe Nwe Htay Win ◽  
Bao Jianmin ◽  
Cui Gang ◽  
Saif Ur Rehman
Keyword(s):  
Web Service ◽  
Service Discovery ◽  
Feasible Solution ◽  
Evaluation Criteria ◽  
The Other ◽  
Discovery Process ◽  
User Request ◽  
Adaptive Qos ◽  
Concept Attribute ◽  
Self Adaptive

In recent years, although semantic has been widely used in service discovery mechanisms, it still needs to exploit all semantic aspects included in service documents so that the discovered service can highly be relevant with user request. Moreover, it also needs to consider self-adaptability in discovering the services which can adapt to searching conditions or parameters in order to find other suitable and potential services if no feasible solution could exactly satisfy user QoS requirements. Therefore, this paper proposes a novel self-adaptive QoS-based service discovery mechanism which can adapt the discovery process with the help of semantically structured ontology trees if unexpected results are encountered. The discovery process matches the equivalences between service advertisement and requirement using three similarity evaluation criteria namely concept, attribute and constraint similarity. This discovery process is repeated until feasible solution is found and a set of most suitable services are returned to the users. The authors prototype their system called SQoSD to evaluate the efficiency and adaptability compared with OWLS-CPS and RQSS. The experimental results prove that our mechanism is superior to the other compared mechanisms.

Rigidity of the Weyl chamber flow, and vanishing theorems of Matsushima and Weil

2009 ◽  
Vol 29 (4) ◽  
pp. 1273-1288 ◽  
Author(s):  
MASAHIKO KANAI
Keyword(s):  
Additional Condition ◽  
The Other ◽  
Weyl Chamber ◽  
Vanishing Theorems ◽  
Compact Lie Group ◽  
Infinitesimal Rigidity ◽  
Extension Theorems ◽  
Whole Space ◽  
Higher Rank ◽  
The One

AbstractThe aim of the present paper is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank non-compact Lie group, on the other. The connection is established via ‘transverse extension theorems’: roughly speaking, they claim that a tangential 1-form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1-form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

scholarly journals TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES

1999 ◽  
Vol 11 (03) ◽  
pp. 267-302 ◽  
Author(s):  
J.-P. ANTOINE ◽  
F. BAGARELLO ◽  
C. TRAPANI
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Product Space ◽  
Function Spaces ◽  
Partial Algebra ◽  
Inner Product Space ◽  
Inner Product ◽  
Partial Algebras ◽  
Amalgam Spaces ◽  
Locally Convex

Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).

scholarly journals For the Renowal Theology of Sacramnetal Priesthood

2020 ◽  
Vol 57 ◽  
pp. 245-264
Author(s):  
Marek Jan Tatar
Keyword(s):  
The Other ◽  
Special Importance ◽  
Pope Francis ◽  
Essential Aspect ◽  
Whole Space ◽  
Key Issues ◽  
Ongoing Formation ◽  
The Church ◽  
Priestly Spirituality

The sacrament of priesthood within the whole space of the development of the Church and its presence in civilisation is one of the key issues. It proves its meaning as well as the necessity of undertaking an ongoing reflection in the context of challenges resulting from the civilisation development. Theology of priesthood is also an essential aspect that has a multi-dimension character and, as such, is a subject of various fields of theology as well as non-theological ones. A reflection upon its relation to a common priesthood of all the faithful, resulting from the sacrament of Baptism, comes into special importance nowadays. Present-day challenges resulting from the development of culture post-modernity require a clear and precise drawing of the essence of sacramental priesthood. The Sacrament of Orders which defines the character and charisma of the called one brings the inseparable sacramental bond with the Christ the Highest and the Only Patriarch. We can find a proper charismatic identity of priesthood in this relation. The other dimension of this charisma is the mission, in which a priest acts in persona Christi. The dual charismatic dimension makes a proper way of making out and understanding the identity of a priest. It means that a priest cannot be substituted in his vocation and the authority which he receives in The Sacrament of Holy Orders and the unity with his bishop. Properly understood and made out identity needs the competent preparation and formation of the candidates to the priesthood, those who have already received Orders and those who are responsible for it alike. All dimensions of formation must be properly integrated. The essential integrating element in the process of ongoing formation is specific priestly spirituality. It means that the fact who a priest is, and then what his mission is, results from the unity of a priest with Christ. The already mentioned civilisation challenges require permanent studies of the ways and methods of the formation. This way the process of formation defends itself from naturalistic or spiritualistic one-sidedness, which a present Pope Francis reminded of, when he said about two “subtle enemies of sanctity”, which are “a present-day Gnosticism” and “a present-day Pelagianism".  

Representability of invariant positive sesquilinear forms on partial *-algebras

1990 ◽  
Vol 108 (2) ◽  
pp. 337-353 ◽  
Author(s):  
J.-P. Antoine ◽  
A. Inoue
Keyword(s):  
Partial Algebra ◽  
Sesquilinear Forms ◽  
Sesquilinear Form ◽  
Partial Algebras ◽  
The Relationship

AbstractWe consider invariant positive sesquilinear forms on a (partial) *-algebra A without unit. First we investigate the relationship between extendability and representability for such a form ø; in particular we discuss under which conditions the two concepts are equivalent. Then we introduce the notions of weak representability and strict unrepresentability, and we show that every fully invariant positive sesquilinear form on A × A is uniquely decomposed into a weakly representable part and a strictly unrepresentable part.

Three Aramaic seals of the Achaemenid period

1986 ◽  
Vol 118 (1) ◽  
pp. 21-29
Author(s):  
S. Shaked ◽  
J. Naveh
Keyword(s):  
The Other ◽  
Bottom Line ◽  
Double Line ◽  
Whole Space ◽  
Image Position ◽  
Upper Register

This seal, of unknown provenance, has an Aramaic inscription which is engraved on a scaraboid hematite pierced lengthwise. It measures 17×13 mm, with 9 mm of thickness. The oval surface, which is slightly damaged at one point, is divided by a double line into two registers. Six letters are engraved in the upper, and five in the lower register, giving the following reading:The letters are fairly large and fill the whole space. All the letters in the upper register stand at the same height on the double line. Normally, however, lamed is higher than the ceiling line of the other letters, while nun and taw are usually drawn with a stroke which goes below the bottom line formed by the other letters. In the lower register the taw and the two nuns seem to go farther down than the alef and the dalet.

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