scholarly journals Real weights, bound states and duality orbits

2016 ◽  
Vol 31 (01) ◽  
pp. 1550218 ◽  
Author(s):  
Alessio Marrani ◽  
Fabio Riccioni ◽  
Luca Romano
Keyword(s):  
Symmetry Group ◽  
Bound States ◽  
Specific Weight ◽  
The Other ◽  
Real Form ◽  
Real Numbers ◽  
The Real ◽  
Duality Symmetry ◽  
Infinite Sequences ◽  
Extremal Black Holes

We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits–Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both [Formula: see text] magic Maxwell–Einstein supergravities and the semisimple infinite sequences of [Formula: see text] and [Formula: see text] theories in [Formula: see text] and [Formula: see text] are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally noncompact and therefore all the weights are real, the stratification is due to the presence of weights of different lengths, while in the other cases it is due to the presence of complex weights.

scholarly journals MEMBANGUN SEMANGAT KERASULAN REMAJA KATOLIK DALAM KONTEKS MASYARAKAT PLURALIS DI INDONESIA

2017 ◽  
Vol 17 (9) ◽  
pp. 3-14
Author(s):  
Agustinus Supriyadi
Keyword(s):  
Logical Consequence ◽  
Cross Cultural ◽  
The Other ◽  
Real Form ◽  
Pluralistic Society ◽  
The Real ◽  
Self Discovery ◽  
The One ◽  
The Church

Catholic teens Indonesia is part of the Church in Indonesia and the Indonesian people. Indonesia consists of thousands of islands that stretched from Sabang to Merauke. This fact opens the possibility of a fairly wide occurrence of the encounter between cultures and simultaneous cross-cultural. This diversity is certainly a logical consequence to an enrichment of civilizations and diversity (plurality), although also contains elements of the loss. Plurality of Indonesian society on the one hand can make the Catholic teens swept away in the swift currents of the community to lose our identity or conflict. However Plurality can also awaken in the Catholic teen award nature between one race to the other races, between ethnic or tribal one with the other tribes, between groups with one another. In a pluralistic society such as this, the Catholic teens called to the apostolate. Through the act of self-discovery, live in love and have a sense of tolerance of differences is the real form of the apostolate.

Some James numbers of Stiefel manifolds

1982 ◽  
Vol 92 (1) ◽  
pp. 139-161 ◽  
Author(s):  
Hideaki Ōshima
Keyword(s):  
The Other ◽  
Stiefel Manifold ◽  
Complex Numbers ◽  
Real Numbers ◽  
The Real ◽  
Stiefel Manifolds ◽  
Other Hand ◽  
Usual Norm

The purpose of this note is to determine some unstable James numbers of Stiefel manifolds. We denote the real numbers by R, the complex numbers by C, and the quaternions by H. Let F be one of these fields with the usual norm, and d = dimRF. Let On, k = On, k(F) be the Stiefel manifold of all orthonormal k–frames in Fn, and q: On, k → Sdn−1 the bundle projection which associates with each frame its last vector. Then the James number O{n, k} = OF{n, k} is defined as the index of q* πdn−1(On, k) in πdn−1(Sdn−1). We already know when O{n, k} is 1 (cf. (1), (2), (3), (13), (33)), and also the value of OK{n, k} (cf. (1), (13), (15), (34)). In this note we shall consider the complex and quaternionic cases. For earlier work see (11), (17), (23), (27), (29), (31) and (32). In (27) we defined the stable James number , which was a divisor of O{n, k}. Following James we shall use the notations X{n, k}, Xs{n, k}, W{n, k} and Ws{n, k} instead of OH{n, k}, , Oc{n, k} and respectively. In (27) we noticed that O{n, k} = Os{n, k} if n ≥ 2k– 1, and determined Xs{n, k} for 1 ≤ k ≤ 4, and also Ws{n, k} for 1 ≤ k ≤ 8. On the other hand Sigrist (31) calculated W{n, k} for 1 ≤ k ≤ 4. He informed the author that W{6,4} was not 4 but 8. Since Ws{6,4} = 4 (cf. § 5 below) this yields that the unstable James number does not equal the stable one in general.

Quadratic forms ‘à la’ local theory

1967 ◽  
Vol 63 (3) ◽  
pp. 579-586 ◽  
Author(s):  
A. Fröhlich
Keyword(s):  
Quadratic Forms ◽  
The Other ◽  
Local Theory ◽  
Real Numbers ◽  
The Real ◽  
Other Hand ◽  
Non Local ◽  
Characteristic 2 ◽  
The One ◽  
Adic Case

In this note (cf. sections 3, 4) I shall give an axiomatization of those fields (of characteristic ≠ 2) which have a theory of quadratic forms like the -adic numbers or like the real numbers. This leads then, for instance, to a generalization of the well-known theorems on -adic forms to a wider class of fields, including non-local ones. The main purpose of the exercise is, however, to separate out the roles of the arithmetic in the underlying field, on the one hand, which solely enters into the verification of the axioms, and of the ordinary algebra of quadratic forms on the other hand. The resulting clarification of the structure of the theory is of interest even in the known -adic case.

scholarly journals Orbits in nonsupersymmetric magic theories

2019 ◽  
Vol 34 (32) ◽  
pp. 1950190
Author(s):  
Alessio Marrani ◽  
Luca Romano
Keyword(s):  
Bound States ◽  
Specific Weight ◽  
Jordan Algebras ◽  
Complex Numbers ◽  
Split Quaternions ◽  
Asymptotically Flat ◽  
Triple Systems ◽  
Duality Symmetry ◽  
Maximal Supergravity ◽  
Consistent Truncations

We determine and classify the electric-magnetic duality orbits of fluxes supporting asymptotically flat, extremal black branes in [Formula: see text] space–time dimensions in the so-called nonsupersymmetric magic Maxwell–Einstein theories, which are consistent truncations of maximal supergravity and which can be related to Jordan algebras (and related Freudenthal triple systems) over the split complex numbers [Formula: see text] and the split quaternions [Formula: see text]. By studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the electric-magnetic duality symmetry group, we obtain that, as for the case of maximal supergravity, in magic nonsupersymmetric Maxwell–Einstein theories there is no splitting of orbits, namely there is only one orbit for each nonmaximal rank element of the relevant Jordan algebra (in [Formula: see text] and 6) or of the relevant Freudenthal triple system (in [Formula: see text]).

scholarly journals Intersections of Real Closed Fields

1980 ◽  
Vol 32 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Thomas C. Craven
Keyword(s):  
Galois Group ◽  
General Class ◽  
Entire Functions ◽  
Algebraic Closure ◽  
Careful Study ◽  
Real Numbers ◽  
The Real ◽  
Real Closed Fields ◽  
Closed Fields ◽  
Infinite Sequences

In this paper we wish to study fields which can be written as intersections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hereditarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythagorean fields by Becker [1]), with this more general class of fields sometimes mentioned in passing. We shall give several characterizations of this class in the next two sections. In § 2 we will be concerned with Gal , the Galois group of an algebraic closure F over F. We also relate the fields to the existence of multiplier sequences; these are infinite sequences of elements from the field which have nice properties with respect to certain sets of polynomials. For the real numbers, they are related to entire functions; generalizations can be found in [3].

Hidden “holes” in the capital of banks and the supply of credit to the real sector of economy

2018 ◽  
pp. 49-68 ◽  
Author(s):  
M. E. Mamonov
Keyword(s):  
Credit Risk ◽  
The Other ◽  
Real Sector ◽  
Capital Management ◽  
Loan Loss ◽  
Short Term ◽  
The Real ◽  
Ex Post ◽  
The One

Our analysis documents that the existence of hidden “holes” in the capital of not yet failed banks - while creating intertemporal pressure on the actual level of capital - leads to changing of maturity of loans supplied rather than to contracting of their volume. Long-term loans decrease, whereas short-term loans rise - and, what is most remarkably, by approximately the same amounts. Standardly, the higher the maturity of loans the higher the credit risk and, thus, the more loan loss reserves (LLP) banks are forced to create, increasing the pressure on capital. Banks that already hide “holes” in the capital, but have not yet faced with license withdrawal, must possess strong incentives to shorten the maturity of supplied loans. On the one hand, it raises the turnovers of LLP and facilitates the flexibility of capital management; on the other hand, it allows increasing the speed of shifting of attracted deposits to loans to related parties in domestic or foreign jurisdictions. This enlarges the potential size of ex post revealed “hole” in the capital and, therefore, allows us to assume that not every loan might be viewed as a good for the economy: excessive short-term and insufficient long-term loans can produce the source for future losses.

ANALYTICAL INDICATOR. ANALYSIS OF THE REAL STATE OF DYNAMICS OF MORTALITY OF THE POPULATION OF RUSSIA FROM MALIGNANT TUMORS AND CHANGES IN ITS STRUCTURE

2019 ◽  
Vol 65 (2) ◽  
pp. 205-219 ◽  
Author(s):  
V. Merabishvili
Keyword(s):  
Malignant Tumors ◽  
Specific Weight ◽  
Mortality Rates ◽  
Retirement Age ◽  
Medium Term ◽  
Age Composition ◽  
The Real ◽  
Indicator Analysis ◽  
The Difference ◽  
Real State

The mortality rate is one of the most important criteria for assessing the health of the population. However, it is important to use analytical indicators correctly, especially when evaluating time series. The value of the “gross” mortality is closely linked with a specific weight of persons of elderly and senile ages. All international publications (WHO, IARC, territorial cancer registers) assess the dynamics of morbidity and mortality only by standardized indicators that eliminate the difference in the age composition of the compared population groups. In Russia, from 1960 to 2017, the share of people of retirement age has increased more than 2 times. The structure of mortality from malignant tumors has changed dramatically. The paper presents the dynamics of gross and standardized mortality rates from malignant tumors in Russia and in all administrative territories. Shows the real success of the Oncology service. The medium-term interval forecast until 2025 has been calculated.

scholarly journals New non-extremal and BPS hairy black holes in gauged $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 8 supergravity

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Andres Anabalon ◽  
Dumitru Astefanesei ◽  
Antonio Gallerati ◽  
Mario Trigiante
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Boundary Conditions ◽  
Charged Black Hole ◽  
Dual Theory ◽  
Real Numbers ◽  
Hairy Black Holes ◽  
Interpolation Parameter ◽  
Black Hole Solutions ◽  
Extremal Black Holes

Abstract In this article we study a family of four-dimensional, $$ \mathcal{N} $$ N = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged $$ \mathcal{N} $$ N = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the $$ \mathcal{N} $$ N = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

Shuffling of Linear Orders

1995 ◽  
Vol 38 (2) ◽  
pp. 223-229
Author(s):  
John Lindsay Orr
Keyword(s):  
Ordered Set ◽  
Linear Orders ◽  
Real Numbers ◽  
The Real ◽  
Linearly Ordered Set

AbstractA linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

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