Towards Verification of Constituent Systems through Automated Proof

DEFF Research Database (Denmark)

Couto, Luis Diogo Monteiro Duarte; Foster, Simon; Payne, R

2014-01-01

This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state invariants and operation preconditions, which can be used...... to specify contractual obligations on the constituent systems of a SoS. To support verification of these obligations we have developed a proof obligation generator and theorem prover plugin for Symphony. The latter uses the Isabelle/HOL theorem prover to automatically discharge the proof obligations arising...... from a CML model. Our hope is that the resulting proofs can then be used to formally verify the conformance of each constituent system, which is turn would result in a dependable SoS....

OTTER, Resolution Style Theorem Prover

International Nuclear Information System (INIS)

McCune, W.W.

2001-01-01

1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands

Bit-Blasting ACL2 Theorems

Directory of Open Access Journals (Sweden)

Sol Swords

2011-10-01

Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.

Formal System Verification - Extension 2

Science.gov (United States)

2012-08-08

vision of truly trustworthy systems has been to provide a formally verified microkernel basis. We have previously developed the seL4 microkernel...together with a formal proof (in the theorem prover Isabelle/HOL) of its functional correctness [6]. This means that all the behaviours of the seL4 C...source code are included in the high-level, formal specification of the kernel. This work enabled us to provide further formal guarantees about seL4 , in

Formal Development of the HRP Prover - Part 1: Syntax and Semantics

International Nuclear Information System (INIS)

Sivertsen, Terje

1996-01-01

This report describes the formal development of a new version of the HRP Prover. The new version of the tool will have functionality almost identical to the current version, but is developed in accordance to established principles for applying algebraic specification in formal software development. The development project provides results of relevance to the formal development of a wide range of language-oriented tools, including programming language compilers, as well as to the automatic generation of code from specifications. Since the overall scope of this report is the analysis of algebraic specifications, emphasis is given to topics related to what is usually understood as the ''front end'' of compilers. This includes lexical and syntax analysis of the specifications, static semantics through type checking, and dynamic semantics through evaluation. All the different phases are specified in algebraic specification and supported by the current version of the HRP Prover. In subsequent work, the completed parts of the new version will complement the tool support in the development. The work presented will be followed up by formal specification of theorem proving and transformation, as well as code generation into conventional programming languages. The new version of the HRP Prover is incrementally developed in coherence with the specifications produced in these activities. At the same time, the development of the tool demonstrates the efficient use of the methodology through real application on an increasingly important class of software. (author)

ISABELLE control system: design concepts

International Nuclear Information System (INIS)

Humphrey, J.W.

1979-01-01

ISABELLE is a Department of Energy funded proton accelerator/storage ring being built at Brookhaven National Laboratory (Upton, Long Island, New York). It is large (3.8 km circumference) and complicated (approx. 30,000 monitor and control variables). It is based on superconducting technology. Following the example of previous accelerators, ISABELLE will be operated from a single control center. The control system will be distributed and will incorporate a local computer network. An overview of the conceptual design of the ISABELLE control system will be presented

Small-angle physics at ISABELLE

International Nuclear Information System (INIS)

Aronson, S.H.

1981-01-01

ISABELLE will be commissioned a few years after the anti p p colliders, whose plans and first results have been presented here. A look at the design goals for ISABELLE reveals that the two salient features offered in compensation for the later turn-on are high luminosity and (2 x 10 5 -10 6 mb -1 sec -1 ) and the number of intersections available for physics. With expected Z 0 detection rates of in UA1, it is clear that all but the most rudimentary features of the standard picture will remain obscure until ISABELLE-like luminosity is available. Some nonstandard models will be hard to distinguish from the standard one until high statistics can be accumulated above the masses of the standard vector bosons. The availability of a relatively large number of intersections at ISABELLE means that there will be room for some highly specific setups which can capitalize on the high luminosity in high-precision or rare-process studies

ISABELLE insertion quadrupoles

International Nuclear Information System (INIS)

Kaugerts, J.; Polk, I.; Sampson, W.; Dahl, P.F.

1979-01-01

Beam focussing and control at the beam intersection regions of ISABELLE is accomplished by a number of superconducting insertion quadrupoles. These magnets differ from the standard ISABELLE quadrupoles in various ways. In particular, the requirements of limited space near the intersections and aperture for beam extraction impose constraints on their configuration. To achieve optimum beam focussing and provide tuning flexibility calls for stronger quadrupole trim windings than those in the standard quadrupoles. The magnetic and mechanical design of the insertion quadrupoles and their associated correction and steering windings to accomplish the above tasks is presented

Prototype and proposed ISABELLE dipoles

International Nuclear Information System (INIS)

McInturff, A.D.; Sampson, W.B.; Robins, K.E.; Dahl, P.F.; Damm, R.

1977-01-01

Data are presented on the latest dipole prototypes to update the operational parameters possible for ISABELLE. This data base will constantly expand until the start of construction of the storage rings. The data will include field quality, stray field magnitudes, quench temperature and propagation times, protection capabilities singly and in multiple units, maximum central fields obtained and training behavior. Performance of the dipoles versus temperature and mode of refrigeration will be discussed. The single layer cosine theta turns distribution coils' parameters are better than those required for the operation of the 200 x 200 GeV version of ISABELLE. The double layer prototype has exceeded the magnetic field performance and two dimensional quality of field needed for the 400 x 400 GeV version of ISABELLE

Analysis of cooldown performance for Isabelle helium refrigerator

International Nuclear Information System (INIS)

Wu, K.C.; Brown, D.P.; Moore, R.W.

1982-01-01

The cooldown performance for the ISABELLE Helium refrigerator is analyzed in terms of the relationship between refrigerator and its load. The flow diagram for ISABELLE with its redundant turbines and heat exchangers is given. Cycle description and procedure for cooldown is described with the relationship between a refrigerator and its load illustrated. Pressure vs. temperature for ISABELLE load and the efficiency for a turbine are illustrated. The procedure for modeling the refrigerator and the concepts of maximizing the cooldown capacity are described. The results and discussion are accompanied with T-S diagrams for initial stage of cooldown and refrigerator characteristic at various return temperatures. The ISABELLE refrigerator with its reduncant expanders properly used achieves cooldown capacity well beyond its steady-state capacity. The cooldown rate at this stage relies on the design safety margin, which for the ISABELLE is 50%

A Higher-Order Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José; Winskel, Glynn

2001-01-01

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....

Towards Formal Verification of a Separation Microkernel

Science.gov (United States)

Butterfield, Andrew; Sanan, David; Hinchey, Mike

2013-08-01

The best approach to verifying an IMA separation kernel is to use a (fixed) time-space partitioning kernel with a multiple independent levels of separation (MILS) architecture. We describe an activity that explores the cost and feasibility of doing a formal verification of such a kernel to the Common Criteria (CC) levels mandated by the Separation Kernel Protection Profile (SKPP). We are developing a Reference Specification of such a kernel, and are using higher-order logic (HOL) to construct formal models of this specification and key separation properties. We then plan to do a dry run of part of a formal proof of those properties using the Isabelle/HOL theorem prover.

Reexamination of the ISABELLE box car stacking scheme

International Nuclear Information System (INIS)

Chasman, R.

1975-01-01

Box car stacking of ISABELLE after acceleration of the fundamental frequency in the AGS is reviewed with the present ISABELLE parameters and examined with regard to longitudinal impedence requirements. The scheme results in an impedance tolerance of Z/n less than or equal to 30 Ω compared to Z/n less than or equal to 5 Ω obtained for rf stacking. However, to meet the claimed luminosity, the AGS performance demands are increased above those assumed in the ISABELLE proposal

System description: Isabelle/jEdit in 2014

Directory of Open Access Journals (Sweden)

Makarius Wenzel

2014-10-01

Full Text Available This is an updated system description for Isabelle/jEdit, according to the official release Isabelle2014 (August 2014. The following new PIDE concepts are explained: asynchronous print functions and document overlays, syntactic and semantic completion, editor navigation, management of auxiliary files within the document-model.

Higher-Order Separation Logic in Isabelle/HOLCF

DEFF Research Database (Denmark)

Varming, Carsten; Birkedal, Lars

2008-01-01

We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF. The assertion language is modeled in such a way that one may use any theory defined in Isabelle/HOLCF to construct assertions, e.g., primitive recursion, least o...

ISABELLE. Volume 3. Experimental areas, large detectors

International Nuclear Information System (INIS)

1981-01-01

This section presents the papers which resulted from work in the Experimental Areas portion of the Workshop. The immediate task of the group was to address three topics. The topics were dictated by the present state of ISABELLE experimental areas construction, the possibility of a phased ISABELLE and trends in physics and detectors

Machine-Checkable Timed CSP

Science.gov (United States)

Goethel, Thomas; Glesner, Sabine

2009-01-01

The correctness of safety-critical embedded software is crucial, whereas non-functional properties like deadlock-freedom and real-time constraints are particularly important. The real-time calculus Timed Communicating Sequential Processes (CSP) is capable of expressing such properties and can therefore be used to verify embedded software. In this paper, we present our formalization of Timed CSP in the Isabelle/HOL theorem prover, which we have formulated as an operational coalgebraic semantics together with bisimulation equivalences and coalgebraic invariants. Furthermore, we apply these techniques in an abstract specification with real-time constraints, which is the basis for current work in which we verify the components of a simple real-time operating system deployed on a satellite.

ISABELLE control system

International Nuclear Information System (INIS)

Humphrey, J.W.; Frankel, R.S.; Niederer, J.A.

1980-01-01

Design principles for the Brookhaven ISABELLE control intersecting storage ring accelerator are described. Principal features include a locally networked console and control computer complex, a system wide process data highway, and intelligent local device controllers. Progress to date is summarized

Cerenkov counters at ISABELLE

International Nuclear Information System (INIS)

Ashford, V.; Etkin, A.; Honma, A.; Kostoulas, I.; Lanou, R.; Watts, T.

1978-01-01

Particle mass identification capability will be very important for much of the physics at ISABELLE. It will be required for studying quantum number flow in quark--quark scattering (jet and high P/sub t/ physics), hadronic decays of W's and Z's, and ''onium'' states. It will be essential for detecting and studying ''naked flavor'' states and generally required or at least very useful for most hadronic physics at ISABELLE. The large all-purpose detectors envisioned for ISABELLE require particle identification covering up to 4π solid angle with high multiplicity capability, high rate capability, insensitivity to high magnetic fields, and large dynamic range (1 to 400 GeV/c). In addition, it would be desirable to have this information for on-line event selection. At present there are only four practical methods for doing charged hadron identification: time-of-flight, dE/dX (ionization sampling), transition radiation, and Cerenkov radiation. All these methods need independent momentum determination and are effective over only limited kinematic ranges. Although the status and foreseeable development of these techniques are discussed at length elsewhere their expected capabilities are summarized in order to compare them with Cerenkov techniques. For the sake of argument a 4π steradian detector with an inner radius of 2 m is assumed

ISABELLE half-cell control system

International Nuclear Information System (INIS)

Buxton, W.; Frankel, R.; Humphrey, J.W.

1977-01-01

The primary function of the ISABELLE half-cell control system is to monitor and control the magnet power supplies of the half-cell. In addition, the control system must be flexible enough that it can be expanded to become involved in additional areas such as vacuum and magnetic measurements. A control system based upon AGS control standards, but modified into a development tool for research and electrical engineering support was constructed. Special attention was given to the inherent differences between controlling an ISABELLE and a conventional fast cycling accelerator. The use of FORTRAN and BASIC networks, and microprocessors is reviewed insofar as they pertain to this system. Some general opinions on model control systems, based upon experience, are presented

ISABELLE lattice

International Nuclear Information System (INIS)

Smith, L.

1975-01-01

An analysis is given of a number of variants of the basic lattice of the planned ISABELLE storage rings. The variants were formed by removing cells from the normal part of the lattice and juggling the lengths of magnets, cells, and insertions in order to maintain a rational relation of circumference to that of the AGS and approximately the same dispersion. Special insertions, correction windings, and the working line with nonlinear resonances are discussed

Process control for the ISABELLE system

International Nuclear Information System (INIS)

Frankel, R.; Herman, A.; Stattel, P.; Warkentien, R.

1981-01-01

A low cost, highly reliable control system has been developed for use in the radiation environment of the ISABELLE ring. The Ultra-High Vacuum installation will consist of approximately 1500 stations - each having 8 readbacks, 4 on-off operations and 4 special functions - distributed over 2.5 mills. The paper will describe a multidrop party line system in which a μp based controller located in a protected environment communicates with up to 25 vacuum stations. All the μp controllers will be linked via the ISABELLE data highway. Mechanical, electronic and software aspects of the system are discussed and performance data from our First Cell model are presented

ISABELLE, accumulators, bunched beams and cosmictrons

International Nuclear Information System (INIS)

Month, M.

1977-01-01

An elaboration of the ISABELLE concept as the model for a high energy, high luminosity proton-proton facility is given. Its place in the total high energy physics program is discussed. Certain features of the ISABELLE design which have not been consolidated, in particular injection and modes of beam operation, are considered. A new scheme is reviewed, one which could provide quick beam turn-on after construction, one in which there is a high probability of reaching and perhaps even exceeding the design objectives, one which should provide comparatively more flexible and reliable operation for physics, and finally one whose presence opens up a window to a much higher energy region. The new system involves the use of a physically separate current accumulator, allowing, therefore, the optimal utilization of the superconducting structures. The fact that an obvious addition to the complex will permit pp collisions in the 4 TeV center-of-mass energy region, which corresponds to an equivalent lab energy of approximately 10 16 eV, i.e., cosmic ray energies, prompts the added structure to be referred to as the COSMICTRON. The facility operated in the ''new'' manner proposed is considered to be ''the best ISABELLE that can be built.''

ISABELLE. Volume 4. Detector R and D

International Nuclear Information System (INIS)

1981-01-01

Workshop participants were asked to assess the current status of detector R and D in terms of the specific needs for ISABELLE experiments: the demands of high particle rates, extremely selective triggers on complex and rare events, and the economics of large detector systems. The detailed results of working groups convened to consider specific areas of detector development are presented. The key points of this assessment, as regards the continuing R and D program for ISABELLE are summarized here. Twenty-six items from the volume were prepared separately for the data base, along with five items previously prepared

ISABELLE. Volume 4. Detector R and D

Energy Technology Data Exchange (ETDEWEB)

1981-01-01

Workshop participants were asked to assess the current status of detector R and D in terms of the specific needs for ISABELLE experiments: the demands of high particle rates, extremely selective triggers on complex and rare events, and the economics of large detector systems. The detailed results of working groups convened to consider specific areas of detector development are presented. The key points of this assessment, as regards the continuing R and D program for ISABELLE are summarized here. Twenty-six items from the volume were prepared separately for the data base, along with five items previously prepared. (GHT)

Vacuum system for ISABELLE

International Nuclear Information System (INIS)

Hobson, J.P.

1975-01-01

An analysis is presented of the proposed vacuum system for the planned ISABELLE storage rings with respect to acceptability and practicality from the vacuum viewport. A comparison is made between the proposed vacuum system and the vacuum system at the CERN ISR, and some comments on various design and operational parameters are made

Computer facilities for ISABELLE data handling

International Nuclear Information System (INIS)

Kramer, M.A.; Love, W.A.; Miller, R.J.; Zeller, M.

1977-01-01

The analysis of data produced by ISABELLE experiments will need a large system of computers. An official group of prospective users and operators of that system should begin planning now. Included in the array will be a substantial computer system at each ISABELLE intersection in use. These systems must include enough computer power to keep experimenters aware of the health of the experiment. This will require at least one very fast sophisticated processor in the system, the size depending on the experiment. Other features of the intersection systems must be a good, high speed graphic display, ability to record data on magnetic tape at 500 to 1000 KB, and a high speed link to a central computer. The operating system software must support multiple interactive users. A substantially larger capacity computer system, shared by the six intersection region experiments, must be available with good turnaround for experimenters while ISABELLE is running. A computer support group will be required to maintain the computer system and to provide and maintain software common to all experiments. Special superfast computing hardware or special function processors constructed with microprocessor circuitry may be necessary both in the data gathering and data processing work. Thus both the local and central processors should be chosen with the possibility of interfacing such devices in mind

Introduction to “Artistic Media and Music Therapy” by Isabelle Frohne-Hagemann

DEFF Research Database (Denmark)

Bonde, Lars Ole

2005-01-01

Introduktion til en musikterapiteoretisk artikel af Isabelle Frohne-Hagemann - i artikelserien INTERNATIONAL ARCHIVES—ON THEORY BUILDING IN MUSIC THERAPY......Introduktion til en musikterapiteoretisk artikel af Isabelle Frohne-Hagemann - i artikelserien INTERNATIONAL ARCHIVES—ON THEORY BUILDING IN MUSIC THERAPY...

Magnet and cryogenics for ISABELLE

International Nuclear Information System (INIS)

Thomas, D.B.

1975-01-01

A critical review was made of the present status and future plans of the Brookhaven National Laboratory superconducting magnet program with respect to the planned ISABELLE storage rings. Recommendations are made on possible technical improvements, the future development program, and areas where cost reduction should be sought

ep possibility for ISABELLE

International Nuclear Information System (INIS)

Wilson, R.

1977-01-01

The feasibility of adding an electron ring to ISABELLE is discussed in terms of cost, physics goals, count rate estimates, the detector requirements, and the possibility of producing intermediate bosons. The purpose of adding an electron ring to ISABELLE must be considered to be the study of e + p → e + x, e - p → νx, and e + p → anti νx. Other processes, such as W production, are less interesting for an ep ring than for a pp ring. However, there may be other new particles--such as leptonic quarks--that only turn up here. These processes are, however, exciting. In a 30 day run at L = 10 32 cm -2 sec -1 300 neutrino events are expected at q 2 > 5000 GeV 2 where the propagator is expected to be less than 1 / 4 . Thus the value of the mass in the propagator can be measured to 5%. The ep cross section would be measured over the momentum transfer range 1 2 2 ). This range is large enough that a logarithmic deviation from scaling can be distinguished easily from a power law approach to scaling

Radiation effects at ISABELLE

International Nuclear Information System (INIS)

Sanger, P.A.; Danby, G.T.

1975-01-01

Shielding, radiation damage, and radiation heating at the planned ISABELLE storage rings were considered. Radiation shielding studies were reviewed and were found to be adequate for present day dosage limits. Radiation damage could be encountered in some extreme cases, but is not expected to limit the performance of the superconducting magnets. Experiments to study the effect of radiation heating on actual magnets are recommended

Performance limitations at ISABELLE

International Nuclear Information System (INIS)

Keil, E.

1975-01-01

The transverse stability of coasting beams in the planned ISABELLE storage rings was studied. The beam--beam tune shift limitation at 0.005 can be avoided, and a computer simulation seems to show 0.005 is a pessimistic limit. For beams of reasonable smoothness on the edge, the actual limit should be somewhat higher. Some coupling effects due to the beam--beam interaction are also examined

Characteristics of the ISABELLE vacuum system

International Nuclear Information System (INIS)

Aggus, J.R.; Edwards, D. Jr.; Halama, H.J.; Herrera, J.C.

1977-01-01

A discussion is given of the complete vacuum system of ISABELLE, emphasizing those design characteristics dictated by high vacuum, the avoidance of beam current loss, and the reduction of background. The experimental and theoretical justifications for the design are presented

NaDeA: A Natural Deduction Assistant with a Formalization in Isabelle

DEFF Research Database (Denmark)

Villadsen, Jørgen; Jensen, Alexander Birch; Schlichtkrull, Anders

2017-01-01

We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in Isabelle. The tool is open source software developed in TypeScript...

NaDeA: A Natural Deduction Assistant with a Formalization in Isabelle

DEFF Research Database (Denmark)

Villadsen, Jørgen; Jensen, Alexander Birch; Schlichtkrull, Anders

2015-01-01

We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in Isabelle. The tool is open source software developed in TypeScript...

An exercise in gigantism: muon polarization measurements at ISABELLE

International Nuclear Information System (INIS)

Kasha, H.

1977-01-01

The possibility of carrying out muon polarization measurements at ISABELLE is briefly examined. The reasons for doing such measurements may well range from checking the obvious to exploring the unexpected. A measurement of the longitudinal muon polarization can serve as a check of the W + decay sample, or may serve as a tool to shed additional light on a new state or process. It is concluded that muon polarization measurements at ISABELLE are on the threshold of possibility, especially if one has to decide between widely separated values

ISABELLE: a progress report

Energy Technology Data Exchange (ETDEWEB)

Hahn, H

1980-01-01

This paper discusses the ISABELLE project, which has the objective of constructing a high-energy proton colliding beam facility at Brookhaven National Laboratory. The major technical features of the intersecting storage accelerators with their projected performance are described. Application of over 1000 superconducting magnets in the two rings represents the salient characteristic of the machine. The status of the entire project, the technical progress made so far, and difficulties encountered are reviewed.

ISABELLE: a progress report

International Nuclear Information System (INIS)

Hahn, H.

1980-01-01

This paper discusses the ISABELLE project, which has the objective of constructing a high-energy proton colliding beam facility at Brookhaven National Laboratory. The major technical features of the intersecting storage accelerators with their projected performance are described. Application of over 1000 superconducting magnets in the two rings represents the salient characteristic of the machine. The status of the entire project, the technical progress made so far, and difficulties encountered are reviewed

Report of the radiation group on radiation backgrounds and damage in the ISABELLE intersection regions

International Nuclear Information System (INIS)

Ludlam, T.; Kistiakowsky, V.; Toohig, T.E.

1976-01-01

The Radiation Group was charged to examine radiation aspects of the current ISABELLE design and the projected experimental arrangements. Some samples of questions to be addressed were: (1) how does the overall shielding design impact the experimental design, (2) what backgrounds might be expected from the proposed beam scraping, shaving, etc. schemes, (3) what are the radiation damage considerations for experimental electronics near the beam, and (4) what backgrounds might be expected in an experiment from operation of another experiment in the same or the adjacent intersection region. A review is given based on the ISABELLE Proposal, The Proceedings of the 1975 ISABELLE Summer Study, and the estimate of ISABELLE shielding requirements by Stevens and Thorndike

Isabelle dipole and quadrupole coil configurations

International Nuclear Information System (INIS)

Dahl, P.F.; Hahn, H.

1980-01-01

The coil configurations of the ISABELLE dipole and quadrupole magnets have been reviewed and a number of improvements were suggested for incorporation into the final design. The coil designs are basically single layer multiple block approximations to cosine current distributions, wound from a high aspect ratio non-keystoned braided conductor. The blocks are separated by knife-edge wedges to maximize the quench propagation velocity. The current density variation is obtained by an appropriate distribution of the spacer turns and, to a lesser degree, by the wedge locations. The use of inert turns is necessary to minimize the peak field enhancement both in the ends and in the two dimensional section. Schemes for deriving turns distributions yielding harmonic coefficients satisfying the stringent ISABELLE tolerances on field uniformity, while allowing for simplicity in winding and taking into account quench propagation considerations, will be discussed, as well as our approach to the coil end configuration

Status reports on ISABELLE magnets

International Nuclear Information System (INIS)

Palmer, R.B.; Baggett, N.; Dahl, P.F.

1982-01-01

The design of the ISABELLE Palmer magnets is described. The performance of thirteen such magnets is reported. Average quench fields of 55 kG at 4.5 0 K have been obtained with essentially no training. The magnets can be shown to be limited only by the short sample characteristics of the cable. Required field quality was achieved in the last four magnets

Cerenkov counters at ISABELLE

International Nuclear Information System (INIS)

Etkin, A.; Kostoulas, I.; Leith, D.W.G.S.; Thun, R.

1977-01-01

The Cherenkov counter described for use at Isabelle is a threshold counter in which light is focussed on phototubes. The counter is applicable in large-angle, small-aperture magnetic spectrometers for measurement of particle yields at large p/sub T/. Three of these counters will provide complete π-K-p separation in the range of 7-20 GeV/c. Other Cherenkov counters are discussed and a bibliography of relevant literature on the counters utilizing photoionization is included

Two superconducting storage rings: ISABELLE

International Nuclear Information System (INIS)

Sanford, J.R.

1978-01-01

The general features of the design and the status of the ISABELLE storage ring project at the present time are reported. It brings up to date the results reported at the National Particle Accelerator Conference in March 1977. The most significant change since that time has been an upgrading of the energy of the overall facility, and acceptance of the project by the Department of Energy

Monopole searches at ISABELLE

International Nuclear Information System (INIS)

Giacomelli, G.; Thorndike, A.

1975-01-01

A discussion is given which supports the continuance of the search for magnetic monopoles at ISABELLE, based on the following assumptions: (1) by 1982 monopoles have not been found; (2) this indicates that, if they exist, they are very massive; (3) other monopole properties are as they are usually assumed to be. An experiment to search for dense tracks is described, an outline is given of a monopole collector for induced current detection, and some discussion is given of the multigamma approach

[An artist at the Medical School of Paris: Isabelle Pinson (1769-1855)].

Science.gov (United States)

Boulinier, G

1997-01-01

Born in Paris in 1769, Isabelle Proteau, the future Mrs. Pinson, was the daughter of a couple of servants of a famous family: her father was the footman of the marquis de Jaucourt, and her mother, the maid of Isabelle, both brother and sister of the encyclopedist Louis de Jaucourt. She lost her father very early, but thanks to her godmother Isabelle de Jaucourt, she received a good education and could become a talented painter. Especially a portraitist, she was a pupil of the academicians Vincent (1746-1816) and Regnault (1754-1829), and participated to many exhibitions at the Louvre's Salons from 1796 to 1812. In 1792, she married the artist and anatomist André Pierre Pinson (1746-1828). Among the witnesses were the surgeon Dezoteux and the famous sculptor Houdon. ...

Proton-proton colliding beam facility ISABELLE

International Nuclear Information System (INIS)

Hahn, H.

1980-01-01

This paper attempts to present the status of the ISABELLE construction project, which has the objective of building a 400 + 400 GeV proton colliding beam facility. The major technical features of the superconducting accelerators with their projected performance are described. Progress made so far, difficulties encountered, and the program until completion in 1986 is briefly reviewed

Charged particle identification: Cherenkov counters at ISABELLE

International Nuclear Information System (INIS)

Etkin, A.; Kostoulas, I.; Leith, D.W.G.S.; Thun, R.

1977-01-01

A brief summary is given of a study of Cherenkov counters for ISABELLE. The study was certainy not exhaustive and was meant primarily to suggest future detector development. A substantial research effort is needed in order to insure that Cherenkov counters utilizing photoionization are fully exploited

ISABELLE magnets. A brief description

International Nuclear Information System (INIS)

Dahl, P.F.

1982-01-01

The modified ISABELLE dipole design, adopted in the fall of 1981, is briefly described, and the assembly procedure and performance of initial prototype magnets summarized. The new magnets incorporate a cabled superconductor wound in a two-layer coil configuration, supported by a laminated split iron yoke. In all cases the prototype magnets reach short sample performance on the first quench, and exhibit virtually no training; eddy current effects are negligible as well

ISABELLE: a 400 x 400 GeV proton--proton colliding beam facility

International Nuclear Information System (INIS)

1978-01-01

A conceptual design report is presented for the construction of an Intersecting Storage Accelerator, ISABELLE, to be located at Brookhaven National Laboratory. At this major research facility beams of protons with energies up to 400 GeV will be collided in six experimental areas. At each area particle physicists will install detector apparatus to study the interaction and reaction products for such very high energy collisions. The proposal results from several years of study and development work on such a facility. Topics discussed include: (1) introduction and summary of the proposal; (2) physics at ISABELLE (including physics objectives and typical experiments and detectors); description of ISABELLE (overview; magnetic ring structure and lattice characteristics; performance; beam transfer, stacking, and acceleration; magnet system; refrigeration system; vacuum system; power supplies, instrumentation, and control system; physical plant and experimental halls; and operation and safety); and (3) cost estimate and schedule

ISABELLE: a 400 x 400 GeV proton--proton colliding beam facility

Energy Technology Data Exchange (ETDEWEB)

None

1978-01-01

A conceptual design report is presented for the construction of an Intersecting Storage Accelerator, ISABELLE, to be located at Brookhaven National Laboratory. At this major research facility beams of protons with energies up to 400 GeV will be collided in six experimental areas. At each area particle physicists will install detector apparatus to study the interaction and reaction products for such very high energy collisions. The proposal results from several years of study and development work on such a facility. Topics discussed include: (1) introduction and summary of the proposal; (2) physics at ISABELLE (including physics objectives and typical experiments and detectors); description of ISABELLE (overview; magnetic ring structure and lattice characteristics; performance; beam transfer, stacking, and acceleration; magnet system; refrigeration system; vacuum system; power supplies, instrumentation, and control system; physical plant and experimental halls; and operation and safety); and (3) cost estimate and schedule.

ISABELLE. Volume 2. Physics

International Nuclear Information System (INIS)

1981-01-01

In this 1981 ISABELLE Workshop, for the Physics category, eight groups worked on eight topics. The mission for each group was to survey the status of each topic, ask new questions, and try to answer them. The organizers of each group were responsible for the organization of meetings, discussions and the final reports of the results from each working group. The mission was completed splendidly. The members enthusiastically participated in the group meetings. Each topic was thoroughly surveyed and many new understandings resulted. Twenty-seven individual items were prepared separately for the data base in addition to five previously prepared

ISABELLE: proceedings of the 1981 Summer Workshop. Volume 1. Lectures

International Nuclear Information System (INIS)

Gordon, H.A.

1981-01-01

The ISABELLE Summer Workshop, held at BNL from July 20 through July 31, was attended by 259 physicists representing 72 institutions. The discussions covered experimental areas, large detectors and detector technology, with a primary emphasis on physics opportunities, both with a phased and a full luminosity ISABELLE. There was a consensus that physics with Phase I (E/sub cm/ approx. = 700 GeV and L approx. 2 x 10 31 /cm 2 /sec, with bunched beams) was feasible, important and exciting. It has been known for years that the orthodox gauge theories will be critically tested by studying the W/sup +-/, Z 0 and high p/sub perpendicular to/ phenomena. The Z 0 has a reasonable chance of being found at the anti pp colliders if luminosities reach 10 30 /cm 2 /sec, but its properties will be difficult to decipher. Seeing the W/sup +-/'s or new heavy quarks is less probable and measuring their properties is even less likely. At ISABELLE these phenomena can all be studied with high precision. But the more exciting conclusion which emerged from the workshop was related to the question of what generates the approx. 100 GeV masses of the W's and Z's. The answer could involve Higgs, technicolor, or other particles with masses ranging from 10.8 GeV to 1 TeV, with an intermediate mass scale of 200 to 300 GeV being a possible region of strong interest. Some of these models predict spectacular experimental signatures. It is clear that only ISABELLE with L approx. 10 32 - 10 33 , has an opportunity of addressing and resolving such questions. Twelve papers from volume one were prepared separately for the data base, along with three items previously prepared

Evaluation of ISABELLE full cell ultra high vacuum system

International Nuclear Information System (INIS)

Foerster, C.L.; Briggs, J.; Chou, T.S.; Stattel, P.

1980-01-01

The ISABELLE Full Cell Vacuum System consisting of a 40 m long, by 8.8 cm diameter stainless steel tube pumped by seven pumping stations was assembled and processed for 10 -12 Torr operation. Evaluation and testing of the system and its sub-assemblies has been completed. Detail design of system components and the determination of the conditioning process was completed. The best procedure to rough pump, leak test, vacuum bake the system, condition pumps, degas gauges, turn on ion pumps and flash sublimation pumps was established. Pressures below 2 x 10 -11 Torr are now routinely achieved in normal operation of the Full Cell. This includes pump down after replacement of various components and pump down after back fill with moist unfiltered air. The techniques developed for the Full Cell will be used to build the ISABELLE Ultra High Vacuum System

Prospects for strong interaction physics at ISABELLE. [Seven papers

Energy Technology Data Exchange (ETDEWEB)

Sidhu, D P; Trueman, T L

1977-01-01

Seven papers are presented resulting from a conference intended to stimulate thinking about how ISABELLE could be used for studying strong interactions. A separate abstract was prepared for each paper for inclusion in DOE Energy Research Abstracts (ERA). (PMA)

Alternative dipole magnets for ISABELLE

Science.gov (United States)

Taylor, C.; Althaus, R.; Caspi, S.; Gilbert, W.; Hassenzahl, W. V.; Meuser, R.; Rechen, J.; Warren, R.

1982-05-01

A dipole magnet, intended as a possible alternative for the ISABELLE main ring magnet, was designed. Three layers of FNAL Doubler/Saver conductor were used. Two 1.3-m-long models were built and tested, both with and without an iron core, and in both helium I and helium II. The training behavior, cyclic energy loss, point of quench initiation, and quench velocity were determined. A central field of 6.5 tesla was obtained in He I (4.4 K), and 7.6 tesla in He II (1.8K).

Mechanical design of ISABELLE magnet cryostats

International Nuclear Information System (INIS)

Kassner, D.

1977-01-01

It has been proposed to construct an intersecting storage ring accelerator, ISABELLE, at BNL, consisting of two concentric rings of magnets containing counter-rotating beams of charged particles. Each ring contains 216 dipole magnets and 138 quadrupoles. All magnets are superconducting and operate at a temperature of 4.3 K. A description of the design of the cryostats, including the internal supports, heat shield superinsulation system and the vacuum vessel is given. Details of fabrication techniques are also included

Mechanical properties of ISABELLE superconducting coils

International Nuclear Information System (INIS)

Thompson, P.; Bertsche, A.; Fuhrmann, J.; Greene, A.; Grove, E.; Repeta, L.; Short, F.; Tannenbaum, M.; Wanderer, P.

1981-01-01

As a part of the manufacturing processes, several mechanical measurements are made on ISABELLE dipoles. These are done both to control the process and to provide information for the evaluation of the behavior of the completed magnets. This paper discusses the Young's Modulus (E = 1-3 x 10 6 psi), the thermal contraction of the coil assembly (ΔL/L = 290 +- 17 x 10 -5 at 77 0 K), and the loss of applied prestress with time

Design of a lepton detector for ISABELLE

International Nuclear Information System (INIS)

Burnstein, R.; Carithers, W.C.; Duong-van, M.

1975-01-01

The theoretical background is given for a proposed experiment to detect W mesons using their leptonic decay mode. A lepton detector was designed for use at the planned ISABELLE proton--proton colliding beam storage rings. The general configuration of the detector is shown, and an electron identification module, an electron-hadron calorimeter, methods of muon identification, and an optional central detector (magnetic solenoid spectrometer) are discussed

ISABELLE: a proton-proton colliding beam facility. [Proposal for the construction of ISABELLE

Energy Technology Data Exchange (ETDEWEB)

None

1977-04-01

A proposal is presented for the construction of an Intersecting Storage Accelerator, ISABELLE, to be located at Brookhaven National Laboratory. At this major research facility, colliding beams of protons will be produced and studied by particle physicists. This proposal combines the interests of these particle physicists in exploring a new energy regime with the challenge of building a new research instrument. The proposal results from several years of considering such devices in parallel with extensive developmental work. The proposal is divided into several major parts. Following an introduction is an overall summary of the proposal covering its highlights. Part II contains a thorough discussion of the physics objectives that can be addressed by the storage ring. It begins with an explanation of current theoretical concepts that occupy the curiosity of high energy physicists. Then follows a brief discussion of possible experiments that might be assembled at the interaction regions to test these concepts. The third part of the proposal goes into the details of the design of the intersecting storage accelerators. It begins with a description of the entire facility and the design of the magnet ring structure. The processes of proton beam accumulation and acceleration are thoroughly described. The discussion then turns to the design of the components and subsystems for the accelerator. The accelerator elements are described followed by a description of the physical plant. The cost estimate and time scales are displayed in Part IV. Here the estimate has been based on the experience gained from working with the prototype units at the laboratory. The appendices are an important part of the proposal. The parameter list for the 200 x 200 GeV ISABELLE is carefully documented. An example of a possible research program can be found in an appendix. The performance of prototype units is documented in one of the appendices.

''Conventional'' Cerenkov counters at ISABELLE

International Nuclear Information System (INIS)

Foley, K.J.

1977-01-01

Cherenkov counters to be used with ISABELLE are described. The three counters used in the Hadron Spectrometer can be used to identify particles in the range 10 to 40 GeV/c with pions separated from heavier particles down to approximately 3 GeV/c. A longer spectrometer for 400 x 400 GeV operation should also be used. The spectrometers may be used with CO 2 and H 2 . The range of particle identification of 8 to 60 GeV/c with pions separated from heavier particles down to approximately 5 GeV/c is possible

MAGCOOL: the production cooling facility for ISABELLE magnets

International Nuclear Information System (INIS)

Bamberger, J.A.; Afrashteh, M.; Brown, D.P.; Schneider, W.J.; Sondericker, J.H.; Wu, K.C.

1981-01-01

The ISABELLE proton accelerator uses over one thousand superconducting magnets to guide the particle beams in two circular rings, 3.8 km in circumference. Prior to their installation in the tunnel all magnets must be tested and measured at their 3.8 K operating temperature. This paper describes the refrigeration system, called MAGCOOL, to accomplish this task

ICAM: the ISABELLE control and monitoring system, global overview

International Nuclear Information System (INIS)

Dimmler, D.G.

1975-01-01

A first draft on the definition of the ISABELLE Control and Monitoring System is presented. Emphasis is given on the design strategies and on the proposed architectural concepts. A triangular network has been selected and defined. Some structural consideration of processor and bus structure hardware are given. (U.S.)

Forced flow cooling of ISABELLE dipole magnets

International Nuclear Information System (INIS)

Bamberger, J.A.; Aggus, J.; Brown, D.P.; Kassner, D.A.; Sondericker, J.H.; Strobridge, T.R.

1976-01-01

The superconducting magnets for ISABELLE will use a forced flow supercritical helium cooling system. In order to evaluate this cooling scheme, two individual dipole magnets were first tested in conventional dewars using pool boiling helium. These magnets were then modified for forced flow cooling and retested with the identical magnet coils. The first evaluation test used a l m-long ISA model dipole magnet whose pool boiling performance had been established. The same magnet was then retested with forced flow cooling, energizing it at various operating temperatures until quench occurred. The magnet performance with forced flow cooling was consistent with data from the previous pool boiling tests. The next step in the program was a full-scale ISABELLE dipole ring magnet, 4.25 m long, whose performance was first evaluated with pool boiling. For the forced flow test the magnet was shrunk-fit into an unsplit laminated core encased in a stainless steel cylinder. The high pressure gas is cooled below 4 K by a helium bath which is pumped below atmospheric pressure with an ejector nozzle. The performance of the full-scale dipole magnet in the new configuration with forced flow cooling, showed a 10 percent increase in the attainable maximum current as compared to the pool boiling data

Some notes concerning ISABELLE electronic instrumentation

International Nuclear Information System (INIS)

Schwartz, M.

1976-01-01

A discussion is given to stimulate early thought relative to the electronic instrumentation which will be required at ISABELLE at the inception of its experimental program. This represents a unique opportunity to approach the instrumentation problem rationally, making provisions for most of the needs in the various intersection regions at minimal cost. In particular, as will be seen, it may be possible to develop a number of specialized integrated circuits which will go a long way toward facilitating the rapid acquisition and examination of data

Automatic Construction of Java Programs from Functional Program Specifications

OpenAIRE

Md. Humayun Kabir

2015-01-01

This paper presents a novel approach to construct Java programs automatically from the input functional program specifications on natural numbers from the constructive proofs of the input specifications using an inductive theorem prover called Poiti'n. The construction of a Java program from the input functional program specification involves two phases. The theorem prover is used to construct a higher order functional (HOF) program from the input specification expressed as an existential the...

Access control system for ISABELLE

International Nuclear Information System (INIS)

Potter, K.; Littenberg, L.

1977-01-01

An access system based on the one now in operation at the CERN ISR is recommended. Access doors would presumably be located at the entrances to the utility tunnels connecting the support buildings with the ring. Persons requesting access would insert an identity card into a scanner to activate the system. The request would be autologged, the keybank adjacent to the door would be unlocked and ISABELLE operations would be notified. The operator would then select the door, activating a TV-audio link. The person requesting entry would draw a key from the bank, show it and his film badge to the operator who would enable the door release

Mechanical properties of ISABELLE superconducting coils

Energy Technology Data Exchange (ETDEWEB)

Thompson, P.; Bertsche, A.; Fuhrmann, J.; Greene, A.; Grove, E.; Repeta, L.; Short, F.; Tannenbaum, M.; Wanderer, P.

1981-01-01

As a part of the manufacturing processes, several mechanical measurements are made on ISABELLE dipoles. These are done both to control the process and to provide information for the evaluation of the behavior of the completed magnets. This paper discusses the Young's Modulus (E = 1-3 x 10/sup 6/ psi), the thermal contraction of the coil assembly (..delta..L/L = 290 +- 17 x 10/sup -5/ at 77/sup 0/K), and the loss of applied prestress with time (approx. 20% for times 20 days).

Directed Security Policies: A Stateful Network Implementation

Directory of Open Access Journals (Sweden)

Cornelius Diekmann

2014-05-01

Full Text Available Large systems are commonly internetworked. A security policy describes the communication relationship between the networked entities. The security policy defines rules, for example that A can connect to B, which results in a directed graph. However, this policy is often implemented in the network, for example by firewalls, such that A can establish a connection to B and all packets belonging to established connections are allowed. This stateful implementation is usually required for the network's functionality, but it introduces the backflow from B to A, which might contradict the security policy. We derive compliance criteria for a policy and its stateful implementation. In particular, we provide a criterion to verify the lack of side effects in linear time. Algorithms to automatically construct a stateful implementation of security policy rules are presented, which narrows the gap between formalization and real-world implementation. The solution scales to large networks, which is confirmed by a large real-world case study. Its correctness is guaranteed by the Isabelle/HOL theorem prover.

Psi-calculi in Isabelle

DEFF Research Database (Denmark)

Bengtson, Jesper; Parrow, Joachim; Weber, Tjark

2016-01-01

This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to) the pi-calculus, the applied pi-calculus, and the spi calculus. Psi-calculi are significantly more expressive, yet their semantics is as simple......, an interactive proof assistant designed to facilitate formal reasoning about calculi with binders. Our main contributions are twofold. First, we have developed techniques that allow efficient reasoning about calculi that bind multiple names in Nominal Isabelle. Second, we have adopted these techniques...... to mechanise substantial results from the meta-theory of psi-calculi, including congruence properties of bisimilarity and the laws of structural congruence. To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date....

Superconducting magnets for ISABELLE

International Nuclear Information System (INIS)

Sampson, W.B.

1976-01-01

The application of superconducting magnet technology to high-energy accelerators has been studied at BNL for many years. Recently this effort has focused on the magnet system for the proposed Intersecting Storage Accelerator, ISABELLE. Several full-sized dipole and quadrupole magnets were fabricated and tested. A dipole was successfully operated using a high pressure forced circulation refrigeration system similar to that proposed for the accelerator. This magnet reached a maximum central field of 4.9 T, considerably above the design field of 3.9 T. A quadrupole of similar design was equally successful, achieving a gradient of 71 T/m compared to the design value of 53 T/m. A summary is given of the present status of the magnet development program, and the direction of future work is outlined

Proceedings of the 1977 Isabelle Summer Workshop. [Seventy-four papers

Energy Technology Data Exchange (ETDEWEB)

None

1977-07-18

A report is given of the activities of the 1977 ISABELLE Summer Workshop, held from July 18 to 29, 1977 at the Brookhaven National Laboratory. An abstract was prepared for each of the seventy-four separate presentations for inclusion in DOE Energy Research Abstracts (ERA). (PMA)

Muon shield requirements for ISABELLE at 400 GeV/c

International Nuclear Information System (INIS)

Ludlam, T.; Thorndike, A.M.

1977-01-01

A goodly portion of the ISABELLE ring lies above the existing contours of the land, and so a substantial earth berm is required to shield against penetrating muons which result from proton interactions within the ring. The size and shape of this shield is determined not only by the magnitude of expected proton losses from the circulating beams, but also by the geometry and magnetic structure of the machine, and the proximity of potential muon sources to the site boundary. The cost of constructing this berm is sufficiently great as to warrant detailed attention to the required shield thickness at each point around the ring. The report given updates previous discussions of the subject by incorporating the six-fold geometry and higher energy of the 400 GeV ISABELLE design, and taking advantage of a more refined study of the effects of magnetic deflection on the trajectories of muons produced within the lattice structure of the machine

ISABELLE [Intersecting Storage Accelerators with the adjective belle] physics prospects

International Nuclear Information System (INIS)

1972-01-01

This volume contains a collection of reports on physics prospects at a 200 x 200-GeV proton intersecting storage ring facility (Isabelle or ISA). General topics of papers included are: machine-related topics, general purpose detectors, strong interaction experiments, weak and electromagnetic interaction experiments, and other exotic ideas

Formalizing and proving a typing result for security protocols in Isabelle/HOL

DEFF Research Database (Denmark)

Hess, Andreas Viktor; Modersheim, Sebastian

2017-01-01

or the positive output of a verification tool. However several of these works have used a typed model, where the intruder is restricted to "well-typed" attacks. There also have been several works that show that this is actually not a restriction for a large class of protocols, but all these results so far...... are again pen-and-paper proofs. In this work we present a formalization of such a typing result in Isabelle/HOL. We formalize a constraint-based approach that is used in the proof argument of such typing results, and prove its soundness, completeness and termination. We then formalize and prove the typing...... result itself in Isabelle. Finally, to illustrate the real-world feasibility, we prove that the standard Transport Layer Security (TLS) handshake satisfies the main condition of the typing result....

Security Modeling and Correctness Proof Using Specware and Isabelle

Science.gov (United States)

2008-12-01

working system by the controlled stepwise introduction of implementation design decisions , in such a way that the refined specifications and ultimately... Auxillary Functions for Current Access to check if contains %% a tuple; Also for adding and removing tuples from Current %% Access...but rather design and implementation decisions by Kestrel but were undocumented. When the problems are encountered with proving in Isabelle, first the

Estimating ISABELLE shielding requirements

International Nuclear Information System (INIS)

Stevens, A.J.; Thorndike, A.M.

1976-01-01

Estimates were made of the shielding thicknesses required at various points around the ISABELLE ring. Both hadron and muon requirements are considered. Radiation levels at the outside of the shield and at the BNL site boundary are kept at or below 1000 mrem per year and 5 mrem/year respectively. Muon requirements are based on the Wang formula for pion spectra, and the hadron requirements on the hadron cascade program CYLKAZ of Ranft. A muon shield thickness of 77 meters of sand is indicated outside the ring in one area, and hadron shields equivalent to from 2.7 to 5.6 meters in thickness of sand above the ring. The suggested safety allowance would increase these values to 86 meters and 4.0 to 7.2 meters respectively. There are many uncertainties in such estimates, but these last figures are considered to be rather conservative

Comparison of different methods for liquid level adjustment in tank prover calibration

International Nuclear Information System (INIS)

Garcia, D A; Farias, E C; Gabriel, P C; Aquino, M H; Gomes, R S E; Aibe, V Y

2015-01-01

The adjustment of the liquid level during the calibration of tank provers with fixed volume is normally done by overfill but it can be done in different ways. In this article four level adjustment techniques are compared: plate, pipette, ruler and overfill adjustment. The adjustment methods using plate and pipette presented good agreement with the tank's nominal volume and lower uncertainty among the tested methods

Formalization of the Resolution Calculus for First-Order Logic

DEFF Research Database (Denmark)

Schlichtkrull, Anders

2016-01-01

A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution, it consi......A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution...

The Secret Prover : Proving Possession of Arbitrary Files While not Giving Them Away

NARCIS (Netherlands)

Teepe, Wouter

2005-01-01

The Secret Prover is a Java application which allows a user (A) to prove to another user (B), that A possesses a file. If B also possesses this file B will get convinced, and if B does not possess this file B will gain no information on (the contents of) this file. This is the first implementation

Provability Calculus of Constructions

DEFF Research Database (Denmark)

Nyblad, Kasten

This thesis presents a type system, Provability Calculus of Constructions (PCoC) that can be used for the formalization of logic. In a theorem prover based on the system, the user can extend the prover with new inference rules in a logically consistent manner. This is done by representing PCo...

Nonfree datatypes in Isabelle/HOL: animating a many-sorted metatheory

OpenAIRE

Schropp, Andreas; Popescu, Andrei

2013-01-01

Datatypes freely generated by their constructors are well supported in mainstream proof assistants. Algebraic specification languages offer more expressive datatypes on axiomatic means: nonfree datatypes generated from constructors modulo equations. We have implemented an Isabelle/HOL package for nonfree datatypes, without compromising foundations. The use of the package, and its nonfree iterator in particular, is illustrated with examples: bags, polynomials and λ-terms modulo α-equivalence. ...

Los relatos de mujeres viajeras ¿Una mirada crítica sobre el colonialismo? Isabelle Eberhardt (1877-1904

Directory of Open Access Journals (Sweden)

Abel Albet I Mas

1998-06-01

Full Text Available WOMEN'S TRAVEL NARRATIVES. A CRITICAL GAZE ON COLONIALISM? iSABELLE EBERHARDT (1877-1904 - The aim of this paper is to analyse the life and works of a woman travel writer, Isabelle Eberhardt and to set it within the context of the recent scholarship related to travel narrative, orientalism and gender. In effect, in his important work on orientalism, Said argued that the Orient is an European construct serving an image of the Other that not only defines the Other but also identifies the self as Western. Nevertheless, Said's contribution neglects the heterogenity of colonial discourse and conceals the roles played by women in the colonization process as well as in its representation. On the contrary, recent feminist scholarship focus on the role of European women as cultural agents in the formation of imperial relations and explores women's complicity with colonialism as well as their resistance to it. But most of the research on women travellers has been carried out by English-speaking authors on english-speaking women travellers. This paper, then, tries to contribute to this field by recovering a marginal voice coming from a different place:Isabelle Eberhardt was born in Geneva (although she was of Russian origin, travelled to Tunisia and Algeria and wrote in french. The complex dynamics of complicity and resistance in Western women is very clear in the case of Isabelle. On one hand, she has the reputation of being "an enemy of France" but, on the other, she is central to the colonial encounter. Isabelle transgresses European norms of gender and civilization by dressing as an Arab and embracing Islam, but her self-exploration was made possible by French colonial power, and in the end, she became a player in French imperial politics. The ambivalence towards colonialism that we can observe in Isabelle's life and works (as in many other women travellers openly questions the notion of simple Otherness as presented in Said's work. The intersection of

Mass resolution for lepton pairs at Isabelle

International Nuclear Information System (INIS)

Baltay, C.; Paige, F.E.

1978-01-01

Experiments measuring e + e - and μ + μ-pairs will be the principal way of searching at ISABELLE for the Z 0 and for vector mesons made from new heavy quark-antiquark (Q anti Q ) pairs. Although the best possible mass resolution is clearly of benefit in such experiments, excessive resolution would lead to an unnecessarily large detector. It is believed that a mass resolution of a few percent is appropriate in searching both for the Z 0 and for new Q anti Q states. However, there are some interesting experiments which would require much better mass resolution, of order 1/4% FWHM. 9 references

Crafty cranes, or the feasibility of robots at ISABELLE

International Nuclear Information System (INIS)

Carroll, A.S.

1978-01-01

As currently envisioned, ISABELLE will have to be shut down at regular intervals much shorter than the natural lifetime of the beams in order to allow the experimenters into the six experimental halls to make simple repairs or simple modifications to their apparatus. Much of this downtime and frustration could be avoided if there were a class of radiation workers who could withstand approx. 10 5 rads. Obviously such a class of workers would be robots. The feasibility of such devices is discussed

Magnet power supply for ISABELLE

International Nuclear Information System (INIS)

Nawrocky, R.J.; Frankel, R.F.; Thomas, M.G.

1979-01-01

The power supply system which will energize the superconducting magnets in the ISABELLE machine consists of some 520 computer-programmable power supplies with outputs ranging from 50 A to 4500 A. Most of the power supplies will be used for the correction of field harmonics, orbit correction and adjustment of the machine working line. During acceleration, currents in various magnet correction coils will be controlled in real time to track the main field; all power supplies must be highly stable during the stacking and storage of the beam (in some cases current regulation must be in the order of 0.001%). PS reference programs will be stored in microprocessor based function generators embedded in each power supply. Due to the large amount of stored energy in the system, the magnets must be protected during quenches. Details of the power supply and of the magnet quench protection system are described

Use of hodoscopes at ISABELLE

International Nuclear Information System (INIS)

Alspector, J.; Miller, R.J.

1977-01-01

A major problem for experimenters designing detectors for use at ISABELLE is the high interaction rate, one event every 25 nanoseconds at a luminosity of 10 33 cm -2 sec -1 . Typical multiplicities range from a few at large angles (> approximately 45 0 ) to approximately 10 nearer the forward direction. This implies average rates as high as a particle every few nanoseconds. For experiments which require high luminosities, detectors must be designed which have very short (approximately 1 nsec) response time and/or intercept a small solid angle per element. These requirements are met by fine-grained scintillation counter hodoscopes. However, it is, at present, impractical to maintain a 10,000 element hodoscope array because of the difficulty of light piping, the complexity and expense of maintaining that many phototubes, and the problems of packaging and readout. Several developments which promise to make such large arrays feasible are discussed

Proportional wire calorimeters at ISABELLE

International Nuclear Information System (INIS)

Matthews, J.A.J.

1979-01-01

Gas calorimeters have recently increased in popularity because they provide a simple method of achieving a high degree of calorimeter segmentation with only a modest loss in energy resolution compared with liquid argon or scintillator calorimeters. High radiation levels at ISABELLE will result in gas calorimeter lifetimes similar to those of MWPCs, although the intermediate speed of these devices may cause some resolution degradation due to signal pileup. Schemes for calibration and monitoring gas calorimeters in situ must be evolved and will presumably utilize a combination of pulsers, imbedded 55 Fe sources, etc. Most of the recent development work on gas calorimeters has been centered on electromagnetic (em) calorimetry for large detectors at CESR and PEP. Data on the performance of gas calorimeters are given and compared with the liquid argon results of Hitlin et al. The hadronic gas calorimeter results of Anderson et al. are shown along with typical energy resolution results from various scintillator and liquid argon steel calorimeters

Average neutralization and transverse stability in ISABELLE

International Nuclear Information System (INIS)

Herrera, J.; Zotter, B.

1978-01-01

Clearing of electrons in the vicinity of the axis of a proton beam in the dipoles of a separated function AG-focusing structure is accomplished by transverse crossed-field drift due to the magnetic dipole field and a weak longitudinal electric field. This electric field is generated by potential differences caused by cross section variations of the beam due to variations of the β-functions and dispersion. The resulting radial drift brings the electrons into the off-axis region where they are driven out of the magnets by the usual longitudinal cross-field drift caused by the radial space charge field. The neutralization in ISABELLE is then a factor 20 below former estimates, and transverse stability can be obtained by chromaticity adjustments well within the design strengths of the sextupole correction windings

Selection and evaluation of an ultra high vacuum gate valve for Isabelle beam line vacuum system

International Nuclear Information System (INIS)

Foerster, C.L.; McCafferty, D.

1980-01-01

A minimum of eighty-four (84) Ultra High Vacuum Gate Valves will be utilized in ISABELLE to protect proton beam lines from catastrophic vacuum failure and to provide sector isolation for maintenance requirements. The valve to be selected must function at less than 1 x 10 -11 Torr pressure and be bakeable to 300 0 C in its open or closed position. In the open position, the valve must have an RF shield to make the beam line walls appear continuous. Several proposed designs were built and evaluated. The evaluation consisted mainly of leak testing, life tests, thermal cycling, mass spectrometer analysis, and 10 -12 Torr operation. Problems with initial design and fabrication were resolved. Special requirements for design and construction were developed. This paper describes the tests on two final prototypes which appear to be the best candidates for ISABELLE operation

PWCs and drift chambers at ISABELLE

International Nuclear Information System (INIS)

Okuno, H.; Teramoto, Y.; Wheeler, C.D.

1979-01-01

At the 1977 Workshop, attempts were made to predict the behavior of proportional wire chambers at the high particle flux expected at ISABELLE. It was found that chambers running at the now widely used high gas gain would have impaired performance with regard to lifetime, efficiency, stability of gas gain, and position resolution. More information has since become available, and therefore the predictions about these properties are revised in the present study. Improvement can also be expected with much lower gas gain, a possibility that is investigated here in more detail with regard to its effect on position resolution and time resolution. The expected high multiplicity of tracks from a single event, the high event rates, and the requirement for low gas gain necessitate revision of the methods for measuring the second coordinate. Particle identification via measurement of the relativistic rise of energy loss in the chambers has been investigated in more detail than previously, with new data and calculations

Controlled Owicki-Gries Concurrency: Reasoning about the Preemptible eChronos Embedded Operating System

Directory of Open Access Journals (Sweden)

June Andronick

2015-11-01

Full Text Available We introduce a controlled concurrency framework, derived from the Owicki-Gries method, for describing a hardware interface in detail sufficient to support the modelling and verification of small, embedded operating systems (OS's whose run-time responsiveness is paramount. Such real-time systems run with interrupts mostly enabled, including during scheduling. That differs from many other successfully modelled and verified OS's that typically reduce the complexity of concurrency by running on uniprocessor platforms and by switching interrupts off as much as possible. Our framework builds on the traditional Owicki-Gries method, for its fine-grained concurrency is needed for high-performance system code. We adapt it to support explicit concurrency control, by providing a simple, faithful representation of the hardware interface that allows software to control the degree of interleaving between user code, OS code, interrupt handlers and a scheduler that controls context switching. We then apply this framework to model the interleaving behavior of the eChronos OS, a preemptible real-time OS for embedded micro-controllers. We discuss the accuracy and usability of our approach when instantiated to model the eChronos OS. Both our framework and the eChronos model are formalised in the Isabelle/HOL theorem prover, taking advantage of the high level of automation in modern reasoning tools.

ISABELLE: a proposal for construction of a proton--proton storage accelerator facility

International Nuclear Information System (INIS)

1976-05-01

The construction of an Intersecting Storage Accelerator Facility (ISA or ISABELLE) at Brookhaven National Laboratory is proposed. ISABELLE will permit the exploration of proton-proton collisions at center-of-mass energies continuously variable from 60 to 400 GeV and with luminosities of 10 32 to 10 33 cm -2 sec -1 over the entire range. An overview of the physics potential of this machine is given, covering the production of charged and neutral intermediate vector bosons, the hadron production at high transverse momentum, searches for new, massive particles, and the energy dependence of the strong interactions. The facility consists of two interlaced rings of superconducting magnets in a common tunnel about 3 km in circumference. The proton beams will collide at eight intersection regions where particle detectors will be arranged for studying the collision processes. Protons of approximately 30 GeV from the AGS will be accumulated to obtain the design current of 10A prior to acceleration to final energy. The design and performance of existing full-size superconducting dipoles and quadrupoles is described. The conceptual design of the accelerator systems and the conventional structures and buildings is presented. A preliminary cost estimate and construction schedule are given. Possible future options such as proton-antiproton, proton-deuteron and electron-proton collisions are discussed

ISABELLE magnet power supply system performance analysis

International Nuclear Information System (INIS)

Edwards, R.J.

1981-01-01

The power supply system that will energize the superconducting magnets in the ISABELLE 400 x 400 GeV accelerator must supply various voltages and currents. The voltages for the correction winding range from ten to one hundred twenty-five volts unipolar and bipolar with current rating of 50 to 300 amperes. The main field winding requires voltages from 90V (at flattop) to 600V during maximum ramp rate or acceleration cycle. The power supplies are programmable over their full range of output current with a reproducibility error varying from +- 10 ppM to +- 400 ppM of full scale. Included within the reproducibility error are the long and short term stability requirements of the power supplies. The purpose of this paper is to define some of the design goals and outline the approach taken in reaching these goals

Virial theorem and hypervirial theorem in a spherical geometry

International Nuclear Information System (INIS)

Li Yan; Chen Jingling; Zhang Fulin

2011-01-01

The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)

The Non-Signalling theorem in generalizations of Bell's theorem

Science.gov (United States)

Walleczek, J.; Grössing, G.

2014-04-01

Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational

Automated Theorem Proving in High-Quality Software Design

Science.gov (United States)

Schumann, Johann; Swanson, Keith (Technical Monitor)

2001-01-01

The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal "cloning" of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.

The Levinson theorem

International Nuclear Information System (INIS)

Ma Zhongqi

2006-01-01

The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)

Building Program Verifiers from Compilers and Theorem Provers

Science.gov (United States)

2015-05-14

Checking with SMT UFO • LLVM-based front-end (partially reused in SeaHorn) • Combines Abstract Interpretation with Interpolation-Based Model Checking • (no...assertions Counter-examples are long Hard to determine (from main) what is relevant Assertion Main 35 Building Verifiers from Comp and SMT Gurfinkel, 2015

SAT-Based Software Certification

National Research Council Canada - National Science Library

Chaki, Sagar

2006-01-01

... predicate abstraction and validated by generating and proving verification conditions. In addition, the first part of the report proposes the use of theorem provers based on Boolean propositional satisfiability (SAT...

Proposal for construction of a proton--proton storage accelerator facility (Isabelle)

International Nuclear Information System (INIS)

1975-06-01

A proposal is made for the construction of proton storage rings at the Brookhaven Alternating Gradient Synchrotron (AGS) using superconducting magnets for which much of the technology has already been developed. This proton-proton colliding beam facility, ''ISABELLE,'' will provide large increases in both the center-of-mass energy and the luminosity, key machine parameters for high energy physics. The physics potential and the general description of the facility are discussed in detail, and the physical plant layout, a cost estimate and schedule, and future options are given.(U.S.)

The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow

International Nuclear Information System (INIS)

Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J

2011-01-01

The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.

PWCs and drift chambers at ISABELLE

International Nuclear Information System (INIS)

Okuno, H.; Teramoto, Y.; Wheeler, C.D.

1978-01-01

Rate effects in proportional chambers and drift chambers are addressed first. The widely used high-gas-gain chambers would have impaired performance at ISABELLE data rates. Improvement can be expected with lower gas gain, and this possibility is investigated with respect to position and time resolution. Results on chamber lifetime are summarized; space-charge effects, gain saturation, and radiation hardness of electronics are considered. The resolution of drift chambers is discussed in some detail; time resolution, double pulse resolution, and momentum resolution and multiple scattering are included. The expected high multiplicity of tracks from a single event, the high event rates, and the requirement for low gas gain necessitate revision of the methods for measuring the second coordinate. Known methods of two-dimensional point localization are summarized according to spatial accuracy, electronics requirements, and multihit capability. Delay lines, charge division, and cathode strips are considered. Particle identification by means of measurement of the relativistic rise of energy loss by conventional and unconventional means was investigated. 32 references, 3 figures, 4 tables

Attack tree analysis for insider threats on the IoT using isabelle

DEFF Research Database (Denmark)

Kammüller, Florian; Nurse, Jason R. C.; Probst, Christian W.

2016-01-01

The Internet-of-Things (IoT) aims at integrating small devices around humans. The threat from human insiders in "regular" organisations is real; in a fully-connected world of the IoT, organisations face a substantially more severe security challenge due to unexpected access possibilities and info....... On the classified IoT attack examples, we show how this logical approach can be used to make the models more precise and to analyse the previously identified Insider IoT attacks using Isabelle attack trees....

Poncelet's theorem

CERN Document Server

Flatto, Leopold

2009-01-01

Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro

Avalanche photodiodes for ISABELLE detectors

International Nuclear Information System (INIS)

Strand, R.C.

1979-01-01

At ISABELLE some requirements for detecting bursts of photons are not met by standard photomultiplier tubes. The characteristics of immunity to magnetic fields, small size (few mm), low power consumption (approx. 100 mW), insensitivity to optical overloads, and wide dynamic range (approx. 60 dB) are achieved with difficulty, if at all, with PMTs. These are characteristics of the solid state avalanche photodiode (APD), the preferred detector for light-wave communications. Successful field tests with APD detectors stimulated the design of standard optical-fiber communication systems to replace wire carriers by the early 1980's. In other characteristics, i.e., counting rate, pulse-height resolution, effective quantum efficiency, detection efficiency, and reliability, bare APDs are equivalent to standard PMTs. APDs with currently available amplifiers cannot resolve single photoelectrons but they could provide reasonable detection efficiencies and pulse-height resolution for packets of approx. > 100 photons. Commercially available APDs can cost up to 100 times as much as PMTs per active area, but they are potentially much cheaper. Six topics are discussed: (1) detectors for light-wave communication and detectors for particles, (2) avalanche photodiodes, (3) commercially available APDs, (4) dynamic response of PMTs and bare APDs, (5) photon counting with cold APDs, and (6) conclusions and recommendations

Experimental use of neutrinos from ISABELLE beam dumps

International Nuclear Information System (INIS)

Bozoki, G.E.; Thorndike, A.M.; Mann, A.K.

1978-01-01

The technical feasibility and possible applicability of using ISABELLE beam dumps as powerful sources for directed high-energy neutrino bursts are investigated. In the present machine design two dump systems are applied to absorb the extracted fast beams. The expected normal beam extraction rate is 1 to 2 per day, when about (6.3 to 7.5) x 10 14 protons are hitting the external targets during a pulse length of approx. 50 μs. These protons are considered so far to be useless. The neutrinos produced could be used for the following activities: the study of coherent neutrino regeneration, calibration and permanent testing of cosmic-ray and astrophysical neutrino detectors, research on the practical applicability of neutrinos in telecommunication, and certain astro- and geophysical applications. Tailoring the system to meet these activities is illustrated. 6 figures

The Non-Signalling theorem in generalizations of Bell's theorem

International Nuclear Information System (INIS)

Walleczek, J; Grössing, G

2014-01-01

Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the

Fermat's Last Theorem A Theorem at Last!

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...

Triggering at Isabelle; the first 200 nanoseconds

International Nuclear Information System (INIS)

Abshire, G.; Kondo, K.; Sculli, J.; Johnson, R.A.; Morris, G.R.

1978-07-01

At full luminosity of ISABELLE and with an anticipated pp total cross section of 60 mb, there will be, on the average, one interaction every 70 ns. At the other end of the spectrum, it will probably take about 10 ms to store a complete event onto magnetic tape. In between these two extremes comes a triggering scheme which must select the one event out of 14,285,714 that is of interest to the experimenter. In a typical experiment, a certain small number of signals will come into an electronics trailer on cables that are as short as possible and have propagation velocities as high as possible. With these signals a fast decision will be made as to whether the rest of the information coming in on the slower, longer cables should be further processed or not. The typical length of time for this decision is 200 ns. Some of the problems arising during that first 200 ns are considered, and some examples of attempts to solve those problems are given

Towards automatic proofs of lock-free algorithms

OpenAIRE

Fejoz , Loïc; Merz , Stephan

2008-01-01

International audience; The verification of lock-free data structures has traditionally been considered as difficult. We propose a formal model for describing such algorithms. The verification conditions generated from this model can often be handled by automatic theorem provers.

Kopitiam: Modular Incremental Interactive Full Functional Static Verification of Java Code

DEFF Research Database (Denmark)

Mehnert, Hannes

2011-01-01

WearedevelopingKopitiam,atooltointeractivelyprovefull functional correctness of Java programs using separation logic by inter- acting with the interactive theorem prover Coq. Kopitiam is an Eclipse plugin, enabling seamless integration into the workflow of a developer. Kopitiam enables a user to ...

A compact kernel for the calculus of inductive constructions

Indian Academy of Sciences (India)

CIC) implemented inside the Matita Interactive Theorem Prover. The design of the new kernel has been completely revisited since the first release, resulting in a remarkably compact implementation of about 2300 lines of OCaml code. The work ...

ISABELLE magnet support and adjustment system

International Nuclear Information System (INIS)

Buchanan, V.; Kassner, D.; Polk, I.

1979-01-01

The ISABELLE superconducting is supported at the quarter points within a carbon steel vacuum vessel by four fiberglass straps. These are positioned at a small angle to the vertical so that contraction of both the magnet core and the suspension straps do not change the position of the magnet centerline. Two smaller fiberglass straps at each support provide horizontal position location. The fiberglass straps are fabricated of uniaxial epoxy fiberglass tape. Creep tests at room temperature and 1.3 times design load show no extension after one year and there was a factor of safety of 5 in breaking strength. An Engineering Test Model was constructed and cycled to 5 0 K. Heat leak for the eight straps was less than 0.5 W and position stability was within +-0.005''. The vacuum vessel is vertically positioned by means of three jack screws with sliding pads and spherical washers between the top of the jacks and the support boxes. Longitudinal and lateral positioning is done by three horizontal screws at each support box. Three shim plates on the top of the support boxes are used to set the magnetic plane and sockets in two of these are used to set the lateral plane

Frege's theorem

CERN Document Server

Heck, Richard G

2011-01-01

Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a

Complex proofs of real theorems

CERN Document Server

Lax, Peter D

2011-01-01

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...

Linear electrical circuits. Definitions - General theorems; Circuits electriques lineaires. Definitions - Theoremes generaux

Energy Technology Data Exchange (ETDEWEB)

Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)

2005-04-01

The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)

Magnet power supply system for the ISABELLE half-cell prototype

International Nuclear Information System (INIS)

Nawrocky, R.J.

1977-01-01

Due to stringent requirements on the spatial harmonic content of ISABELLE's magnetic field, the magnet power supplies for the half-cell prototype must be dynamically accurate and stable to within 0.01% of their full-scale rating. Depending on the application, the full-scale current of various units comprising the system ranges from +-50 A to 4000 A. The system, as constructed is fully controllable and programmable either manually or with a control computer. The magnet power supply system described was constructed and interconnected with the half-cell computer control equipment. A number of power supply units were tested with inductive test loads in both the manual and the computer control modes. Test results on stability and speed of response indicate that all systems perform according to specifications

Gap and density theorems

CERN Document Server

Levinson, N

1940-01-01

A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie

Summary of activity. Topic I: detectors and experiments. [High-energy detectors for use at ISABELLE

Energy Technology Data Exchange (ETDEWEB)

Marx, J; Ozaki, S

1978-01-01

Results of a workshop studying detectors for Isabelle experimental halls are described. The detectors must be very reliable. Spatial resolution of the tracking detectors must be high to provide accurate measurements of angle and momentum, retain a short resolving time, and show excellent multiparticle handling capability. Included in the study were hodoscopes, drift chambers, proportional chambers, time projection chambers, Cherenkov counters, electromagnetic shower detectors, and hadron calorimeters. Data handling methods were also included in the studies. (FS)

The quantitative Morse theorem

OpenAIRE

Loi, Ta Le; Phien, Phan

2013-01-01

In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.

Simple computer model for the nonlinear beam--beam interaction in ISABELLE

International Nuclear Information System (INIS)

Herrera, J.C.; Month, M.; Peierls, R.F.

1979-03-01

The beam--beam interaction for two counter-rotating continuous proton beams crossing at an angle can be simulated by a 1-dimensional nonlinear force. The model is applicable to ISABELLE as well as to the ISR. Since the interaction length is short compared with the length of the beam orbit, the interaction region is taken to be a point. The problem is then treated as a mapping with the remainder of the system taken to be a rotation of phase given by the betatron tune of the storage ring. The evolution of the mean square amplitude of a given distribution of particles is shown for different beam--beam strengths. The effect of round-off error with resulting loss of accuracy for particle trajectories is discussed. 3 figures

Abstract Object Creation in Dynamic Logic

NARCIS (Netherlands)

I. Grabe (Immo); F.S. de Boer (Frank); W. Ahrendt (Wolfgang); A. Cavalcanti; D.R. Dams

2009-01-01

textabstractIn this paper we give a representation of a weakest precondition calculus for abstract object creation in dynamic logic, the logic underlying the KeY theorem prover. This representation allows to both specify and verify properties of objects at the abstraction level of the

Semantics and logic for security protocols

NARCIS (Netherlands)

Jacobs, B.P.F.; Hasuo, I.

2009-01-01

This paper presents a sound BAN-like logic for reasoning about security protocols with theorem prover support. The logic has formulas for sending and receiving messages (with nonces, public and private encryptions, etc.), and has both temporal and epistemic operators (describing the knowledge of

Isabelle et Marguerite ou les pliures du féminin

Directory of Open Access Journals (Sweden)

Sjef Houppermans

2008-07-01

Full Text Available Isabelle de Charrière (1740-1805 montre dans ses romans épistolaires, pour le contenu comme pour la forme et le style, une préoccupation constante avec la séparation, l’absence et le manque. Ici les Lettres écrites de Lausanne vont nous retenir plus spécifiquement suivant cette perspective. Marguerite Yourcenar (1903-1987 trace partout dans son œuvre les lignes d’un désir qui ne cesse de s’épuiser dans ses pertes et ses failles. C’est plus particulièrement la nouvelle Anna, Soror, histoire d’inceste sur fond de décor baroque, qui exhibe les traces de l’étrangeté familière colorant l’élan fictionnel. Les deux écrivaines se croisent dans un semblable liage scriptural.

Bertrand's theorem and virial theorem in fractional classical mechanics

Science.gov (United States)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Joint Logistics Commanders’ Biennial Software Workshop (4th) Orlando II: Solving the PDSS (Post Deployment Software Support) Challenge Held in Orlando, Florida on 27-29 January 87. Volume 2. Proceedings

Science.gov (United States)

1987-06-01

described the state )f ruaturity of software engineering as being equivalent to the state of maturity of Civil Engineering before Pythagoras invented the...formal verification languages, theorem provers or secure configuration 0 management tools would have to be maintained and used in the PDSS Center to

Final environmental impact statement. Proton--Proton Storage Accelerator Facility (ISABELLE), Brookhaven National Laboratory, Upton, New York

International Nuclear Information System (INIS)

1978-08-01

An Environmental Impact Statement for a proposed research facility (ISABELLE) to be built at Brookhaven National Laboratory (BNL) is presented. It was prepared by the Department of Energy (DOE) following guidelines issued for such analyses. In keeping with DOE policy, this statement presents a concise and issues-oriented analysis of the significant environmental effects associated with the proposed action. ISABELLE is a proposed physics research facility where beams of protons collide providing opportunities to study high energy interactions. The facility would provide two interlaced storage ring proton accelerators, each with an energy up to 400 GeV intersecting in six experimental areas. The rings are contained in a tunnel with a circumference of 3.8 km (2.3 mi). The facility will occupy 250 ha (625 acres) in the NW corner of the existing BNL site. A draft Environmental Impact Statement for this proposed facility was issued for public review and comment by DOE on February 21, 1978. The principal areas of concern expressed were in the areas of radiological impacts and preservation of cultural values. After consideration of these comments, appropriate actions were taken and the text of the statement has been amended to reflect the comments. The text was annotated to indicate the origin of the comment. The Appendices contain a glossary of terms and listings of metric prefixes and conversions and symbols and abbreviations

MVT a most valuable theorem

CERN Document Server

Smorynski, Craig

2017-01-01

This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...

Generalized Dandelin’s Theorem

Science.gov (United States)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

Factor and Remainder Theorems: An Appreciation

Science.gov (United States)

Weiss, Michael

2016-01-01

The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

Abstractions for Fault-Tolerant Distributed System Verification

Science.gov (United States)

Pike, Lee S.; Maddalon, Jeffrey M.; Miner, Paul S.; Geser, Alfons

2004-01-01

Four kinds of abstraction for the design and analysis of fault tolerant distributed systems are discussed. These abstractions concern system messages, faults, fault masking voting, and communication. The abstractions are formalized in higher order logic, and are intended to facilitate specifying and verifying such systems in higher order theorem provers.

The Patchwork Divergence Theorem

OpenAIRE

Dray, Tevian; Hellaby, Charles

1994-01-01

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...

The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

Directory of Open Access Journals (Sweden)

Claude Semay

2015-01-01

Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

Impact of cadmium on forage kale (Brassica oleracea var. viridis cv "Prover") after 3-,10- and 56-day exposure to a Cd-spiked field soil.

Science.gov (United States)

Bernard, Fabien; Dumez, Sylvain; Lemière, Sébastien; Platel, Anne; Nesslany, Fabrice; Deram, Annabelle; Vandenbulcke, Franck; Cuny, Damien

2018-03-15

Cadmium (Cd) is a highly toxic element for living organisms and is widespread in metal-contaminated soils. As organisms which can grow up on these polluted areas, plants have some protection mechanisms against Cd issues. Among the plant kingdom, the Brassicaceae family includes species which are known to be able to tolerate and accumulate Cd in their tissues. In this study, Brassica oleracea var. viridis cv "Prover" was exposed to a range of artificially Cd-contaminated soils (from 2.5 up to 20 mg kg -1 ) during 3, 10, and 56 days and the effects on life traits, photosynthesis activity, antioxidant enzymatic activities were studied. Metal accumulation was quantified, as well as DNA damage, by means of the comet assay and immunodetection of 8-OHdG levels. Globally, B. oleracea was relatively tolerant to those Cd exposures. However, comet assay and detection of 8-OHdG revealed some DNA damage but which are not significant. According to metal accumulation analysis, B. oleracea var. viridis cv Prover could be a good candidate for alternative growing in contaminated areas.

Une reine entre ombres et lumières ou le pouvoir au féminin : le cas d’Isabelle Bourbon, reine d’Espagne, première femme de Philippe IV (1603-1644

Directory of Open Access Journals (Sweden)

Frédérique Sicard

2009-09-01

Full Text Available Le rôle de la Reine et sa relation au pouvoir sont strictement réglementés, mais son influence politique est paradoxalement difficile à apprécier car elle s’exerce à l’ombre de ce qui est permis. Isabelle de Bourbon, née Princesse de France, épouse en 1615 le Prince héritier Philippe d’Espagne et fait partie de ces Reines de l’ombre, peu étudiées. Elevée dans une certaine liberté, le contraste avec la cour d’Espagne et la surveillance de l’omniprésent Favori, le Comte-Duc d’Olivares, lui pèsent d’autant plus. Quel éclairage le cas de la Reine Isabelle permet-il d’apporter à la relation entre genre et pouvoir au Siècle d’Or ? Trois points seront abordés : les tensions et dominations qui se jouent autour du Roi Philippe IV, le poids de la famille, au sens large, indissociable des relations entretenues entre genre et pouvoir. Enfin, nous nous intéresserons à l’activité politique de la Reine Isabelle.The role of French queens and their relation to power were strictly regulated, but their political influence is difficult to assess given the shadows within which they worked. In 1615, Isabelle of Bourbon, born Princess of France, married Philip of Spain and became one of these seldom-studied Queens of the shadows. What illumination does Queen Isabelle’s case bring to the gender-power relationship during the Golden Age? Three points are addressed in the article: the tensions and power dynamics around Philip IV; the weight of the family, in a broad sense, which necessarily affected relations between gender and power. Finally, we will focus on the political activity of Queen Isabelle; her example constitutes a concrete example of women’s power in the Golden Age.

On Krasnoselskii's Cone Fixed Point Theorem

Directory of Open Access Journals (Sweden)

Man Kam Kwong

2008-04-01

Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.

Compte-rendu de : Isabelle Stengers, Penser avec Whitehead, Paris : Seuil, 2002, 582p.

Directory of Open Access Journals (Sweden)

Pierre Cassou-Noguès

2006-05-01

Full Text Available L’ouvrage conjoint un double effort, que résume parfaitement le titre : Penser avec Whitehead. Au départ, l’ouvrage se présente comme un commentaire de l’œuvre de Whitehead. Isabelle Stengers cherche à éclairer les textes, souvent difficiles, de Whitehead et cela par ordre chronologique, pour en particulier analyser le passage de l’épistémologie à la cosmologie et les différentes strates de la cosmologie. Whitehead, qui a rédigé avec Russell les Principia Mathematica, commence son œuvre philo...

Discovering the Theorem of Pythagoras

Science.gov (United States)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

Keller’s theorem revisited

Science.gov (United States)

Ortiz, Guillermo P.; Mochán, W. Luis

2018-02-01

Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.

A Decomposition Theorem for Finite Automata.

Science.gov (United States)

Santa Coloma, Teresa L.; Tucci, Ralph P.

1990-01-01

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

The Classical Version of Stokes' Theorem Revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

2005-01-01

Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...

The Second Noether Theorem on Time Scales

Directory of Open Access Journals (Sweden)

Agnieszka B. Malinowska

2013-01-01

Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.

Nonextensive Pythagoras' Theorem

OpenAIRE

Dukkipati, Ambedkar

2006-01-01

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...

Some approximation theorems

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...

Feasibility of studying large p/sub perpendicular to/ in ISABELLE's wide-angle hall

International Nuclear Information System (INIS)

Aronson, S.; Danby, G.; Engelmann, R.; Foley, K.; McCarthy, R.; Paige, F.; Pope, B.; Thorndike, A.

1979-01-01

The experimental area at 6 o'clock in the present ISABELLE site plan has a configuration suitable for studying particles produced at large angles relative to the beam lines. It is natural to think of housing a program of large p/perpendicular to/ studies in this area. A particular device has been considered, namely a pair of multiparticle spectrometers back-to-back at 90 0 to the beams, as a vehicle for carrying out this program. Enough details are presented to allow for a reasonable test of the planned 6 o'clock area as a site for such experiments. In summer, this study shows that a rather ambitious program of experiments can be performed in this area with some relatively easily implemented changes in the hall design

Pascal’s Theorem in Real Projective Plane

OpenAIRE

Coghetto Roland

2017-01-01

In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.

Pascal’s Theorem in Real Projective Plane

Directory of Open Access Journals (Sweden)

Coghetto Roland

2017-07-01

Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

Science.gov (United States)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

Testing First-Order Logic Axioms in AutoCert

Science.gov (United States)

Ahn, Ki Yung; Denney, Ewen

2009-01-01

AutoCert [2] is a formal verification tool for machine generated code in safety critical domains, such as aerospace control code generated from MathWorks Real-Time Workshop. AutoCert uses Automated Theorem Provers (ATPs) [5] based on First-Order Logic (FOL) to formally verify safety and functional correctness properties of the code. These ATPs try to build proofs based on user provided domain-specific axioms, which can be arbitrary First-Order Formulas (FOFs). These axioms are the most crucial part of the trusted base, since proofs can be submitted to a proof checker removing the need to trust the prover and AutoCert itself plays the part of checking the code generator. However, formulating axioms correctly (i.e. precisely as the user had really intended) is non-trivial in practice. The challenge of axiomatization arise from several dimensions. First, the domain knowledge has its own complexity. AutoCert has been used to verify mathematical requirements on navigation software that carries out various geometric coordinate transformations involving matrices and quaternions. Axiomatic theories for such constructs are complex enough that mistakes are not uncommon. Second, adjusting axioms for ATPs can add even more complexity. The axioms frequently need to be modified in order to have them in a form suitable for use with ATPs. Such modifications tend to obscure the axioms further. Thirdly, speculating validity of the axioms from the output of existing ATPs is very hard since theorem provers typically do not give any examples or counterexamples.

Topological interpretation of Luttinger theorem

OpenAIRE

Seki, Kazuhiro; Yunoki, Seiji

2017-01-01

Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...

High-Assurance Spiral

Science.gov (United States)

2017-11-01

HIGH-ASSURANCE SPIRAL CARNEGIE MELLON UNIVERSITY NOVEMBER 2017 FINAL TECHNICAL REPORT APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED STINFO...MU 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Carnegie Mellon University 5000 Forbes Ave Pittsburgh, PA 15217 8. PERFORMING ORGANIZATION...Approved for Public Release; Distribution Unlimited. Carnegie Mellon Carnegie Mellon HA SPIRAL Code Synthesis KeYmaera X Hybrid Theorem Prover

A note on generalized Weyl's theorem

Science.gov (United States)

Zguitti, H.

2006-04-01

We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

Morley’s Trisector Theorem

Directory of Open Access Journals (Sweden)

Coghetto Roland

2015-06-01

Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].

Riemannian and Lorentzian flow-cut theorems

Science.gov (United States)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

An extended characterisation theorem for quantum logics

International Nuclear Information System (INIS)

Sharma, C.S.; Mukherjee, M.K.

1977-01-01

Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)

The Levy sections theorem revisited

International Nuclear Information System (INIS)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da

2007-01-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets

The Levy sections theorem revisited

Science.gov (United States)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2007-06-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

Definable davies' theorem

DEFF Research Database (Denmark)

Törnquist, Asger Dag; Weiss, W.

2009-01-01

We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....

Green's theorem and Gorenstein sequences

OpenAIRE

Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su

2016-01-01

We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...

Complex integration and Cauchy's theorem

CERN Document Server

Watson, GN

2012-01-01

This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the

The de Finetti theorem for test spaces

International Nuclear Information System (INIS)

Barrett, Jonathan; Leifer, Matthew

2009-01-01

We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.

-Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

Commentaries on Hilbert's Basis Theorem | Apine | Science World ...

African Journals Online (AJOL)

The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...

Choice of harmonic number for the ISABELLE accelerating rf system

International Nuclear Information System (INIS)

Pedersen, F.

1977-01-01

Originally, h = 2 was chosen for the accelerating rf system to avoid growth of coupled bunch mode longitudinal instabilities. The ability to operate ISABELLE in a bunched mode and maintaining six interaction points plus the compatibility with the boxcar transfer scheme suggested for transfer from an eventual future accumulator ring has made it desirable to choose a different harmonic number, namely h = 3. It is shown in the following that the impedance threshold for these instabilities is higher than the impedance limit required during stacking to obtain design performance. The threshold is independent of the harmonic number, so the choice of h is free from an instability point of view, as long as we are below this threshold. For h = 3, the required peak voltage to produce the same acceptance and acceleration rate as the h = 2 system is 35 kV compared to 30 kV for the h = 2 system. The total stored energy in the h = 3 cavities will be less than in h = 2 cavities, so the cost is roughly unchanged. For the above mentioned reasons it is strongly recommended to choose h = 3

Study of factors which affect training in ISABELLE R and D magnets

International Nuclear Information System (INIS)

Wanderer, P.; Bleser, E.; Cottingham, G.

1981-01-01

Five R and D dipole magnets have been assembled with different levels of tangential prestress applied to the windings. Four magnets have trained beyond the ISABELLE 5T operating field. Three have trained to the short sample limit of the superconducting braid. The two magnets with the highest level of tangential prestress required the fewest training quenches to reach 5T. The training history of these R and D magnets is better than that of the eleven industrial magnets. Two of the industrial magnets were trained beyond 4.5T; the others reached fields in the range 3.8T to 4.2T. The industrial magnets had generally lower levels of prestress than the R and D magnets and differed in other important respects as well. These changes were designed to reduce the heat generated by conductor motion due to Lorentz forces. Construction of magnets with the present design has eliminated the largest part of the training quenches seen in the industrial series of magnets

A density Corradi-Hajnal theorem

Czech Academy of Sciences Publication Activity Database

Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.

2015-01-01

Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6

Symbolic logic and mechanical theorem proving

CERN Document Server

Chang, Chin-Liang

1969-01-01

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

Coalgebraic Lindström Theorems

NARCIS (Netherlands)

Kurz, A.; Venema, Y.

2010-01-01

We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,

Equivalent conserved currents and generalized Noether's theorem

International Nuclear Information System (INIS)

Gordon, T.J.

1984-01-01

A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order

Strong versions of Bell's theorem

International Nuclear Information System (INIS)

Stapp, H.P.

1994-01-01

Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption

Geometry of the Adiabatic Theorem

Science.gov (United States)

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

A definability theorem for first order logic

NARCIS (Netherlands)

Butz, C.; Moerdijk, I.

1997-01-01

In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S

On Newton’s shell theorem

Science.gov (United States)

Borghi, Riccardo

2014-03-01

In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

Science.gov (United States)

Moen, David H.; Powell, John E.

2005-01-01

Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

The implicit function theorem history, theory, and applications

CERN Document Server

Krantz, Steven G

2003-01-01

The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...

No-go theorems for the minimization of potentials

International Nuclear Information System (INIS)

Chang, D.; Kumar, A.

1985-01-01

Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness

Tarski Geometry Axioms. Part III

Directory of Open Access Journals (Sweden)

Coghetto Roland

2017-12-01

Full Text Available In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters. Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations the propositions (“Satz” are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2.

Applications of square-related theorems

Science.gov (United States)

Srinivasan, V. K.

2014-04-01

The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.

The matrix Euler-Fermat theorem

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2004-01-01

We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

Formal Verification of Safety Buffers for Sate-Based Conflict Detection and Resolution

Science.gov (United States)

Herencia-Zapana, Heber; Jeannin, Jean-Baptiste; Munoz, Cesar A.

2010-01-01

The information provided by global positioning systems is never totally exact, and there are always errors when measuring position and velocity of moving objects such as aircraft. This paper studies the effects of these errors in the actual separation of aircraft in the context of state-based conflict detection and resolution. Assuming that the state information is uncertain but that bounds on the errors are known, this paper provides an analytical definition of a safety buffer and sufficient conditions under which this buffer guarantees that actual conflicts are detected and solved. The results are presented as theorems, which were formally proven using a mechanical theorem prover.

A proof of Bertrand's postulate

Directory of Open Access Journals (Sweden)

Andrea Asperti

2012-01-01

Full Text Available We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev concerning the distribution of prime numbers, subsuming, as a corollary, Bertrand's postulate.Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of number theory. The proof makes use of most part of the machinery of elementary arithmetics, and in particular of properties of prime numbers, gcd, products and summations, providing a natural benchmark for assessing the actual development of the arithmetical knowledge base.

A Converse to the Cayley-Hamilton Theorem

Indian Academy of Sciences (India)

follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...

Formalization and Implementation of Algebraic Methods in Geometry

Directory of Open Access Journals (Sweden)

Filip Marić

2012-02-01

Full Text Available We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method, their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools and should enable new applications of theorem proving in education.

Converse Barrier Certificate Theorem

DEFF Research Database (Denmark)

Wisniewski, Rafael; Sloth, Christoffer

2013-01-01

This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...

Stacked spheres and lower bound theorem

Indian Academy of Sciences (India)

BASUDEB DATTA

2011-11-20

Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...

Dimensional analysis beyond the Pi theorem

CERN Document Server

Zohuri, Bahman

2017-01-01

Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...

Automated theorem proving theory and practice

CERN Document Server

Newborn, Monty

2001-01-01

As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...

Stable convergence and stable limit theorems

CERN Document Server

Häusler, Erich

2015-01-01

The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...

Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally

OpenAIRE

Salehi, Saeed

2015-01-01

We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.

Generalized Optical Theorem Detection in Random and Complex Media

Science.gov (United States)

Tu, Jing

The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar

Other trigonometric proofs of Pythagoras theorem

OpenAIRE

Luzia, Nuno

2015-01-01

Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.

The Pomeranchuk theorem and its modifications

International Nuclear Information System (INIS)

Fischer, J.; Saly, R.

1980-01-01

A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table

Adiabatic theorem and spectral concentration

International Nuclear Information System (INIS)

Nenciu, G.

1981-01-01

The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru

Nonperturbative Adler-Bardeen theorem

International Nuclear Information System (INIS)

Mastropietro, Vieri

2007-01-01

The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions

A general comparison theorem for backward stochastic differential equations

OpenAIRE

Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.

2010-01-01

A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...

Pythagoras theorem

OpenAIRE

Debattista, Josephine

2000-01-01

Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.

On Comparison Theorems for Conformable Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Mehmet Zeki Sarikaya

2016-10-01

Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

The classical version of Stokes' Theorem revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

2008-01-01

Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....

Unpacking Rouché's Theorem

Science.gov (United States)

Howell, Russell W.; Schrohe, Elmar

2017-01-01

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

Search strategy for theorem proving in artificial systems. I

Energy Technology Data Exchange (ETDEWEB)

Lovitskii, V A; Barenboim, M S

1981-01-01

A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.

Tight closure and vanishing theorems

International Nuclear Information System (INIS)

Smith, K.E.

2001-01-01

Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric

The Osgood-Schoenflies theorem revisited

International Nuclear Information System (INIS)

Siebenmann, L C

2005-01-01

The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned

Preservation theorems on finite structures

International Nuclear Information System (INIS)

Hebert, M.

1994-09-01

This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs

The Interpretability of Inconsistency: Feferman's Theorem and Related Results

NARCIS (Netherlands)

Visser, Albert

This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case

The Interpretability of Inconsistency: Feferman's Theorem and Related Results

NARCIS (Netherlands)

Visser, Albert

2014-01-01

This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case

Outgassing rate of the copper-plated beam tube for ISABELLE

International Nuclear Information System (INIS)

Hseuh, H.C.; Gaudet, E.F.

1981-01-01

The ultrahigh vacuum system of the intersecting storage accelerator, ISABELLE, will consist of two interlaced rings of stainless steel beam tubes with a circumference 2-1/2 miles each. To obtain a good heat conduction during bakeout and to reduce the resistive wall instability during beam operation, a lmm thick copper coating will be electroplated to the outer surface of this 1.5 mm thick beam tube. To minimize the beam loss due to beam-gas collision, the pressure inside the beam tube is required to be 1 x 10 -11 Torr (N 2 equivalent) or less. To achieve this ultrahigh vacuum, the outgassing rate of the 304 LN stainless steel tubes has been reduced to approx. 1 x 10 -13 Torr. l/cm 2 . sec by vacuum firing at 950 0 C for one hour. However, during acid-bath electroplating of copper, significant amount of hydrogen will be reintroduced and trapped in stainless steel which will substantially increase the outgassing rate (to approx. 2 x 10 -12 Torr . l/cm 2 sec). The outgassing characteristics of these copper-plated beam tubes are studied and discussed within the scope of diffusion and energy of activation. Methods to reduce the outgassing rate to an acceptable level (approx. 1 x 10 -13 Torr . l/cm 2 . sec) are also given

Some fixed point theorems in fuzzy reflexive Banach spaces

International Nuclear Information System (INIS)

Sadeqi, I.; Solaty kia, F.

2009-01-01

In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.

The Goldstone equivalence theorem and AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)

2015-08-03

The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....

Two proofs of Fine's theorem

International Nuclear Information System (INIS)

Halliwell, J.J.

2014-01-01

Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities

Reasoning About Higher-Order Relational Specifications

OpenAIRE

Wang , Yuting; Chaudhuri , Kaustuv; Gacek , Andrew; Nadathur , Gopalan

2013-01-01

International audience; The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to encoding side conditions and contexts that occur frequently in structural operational semantics (SOS) style presentations. Specifications are often useful in reasoning about the systems they describe. The Abella theorem prover supports s...

Using simplex method in verifying software safety

Directory of Open Access Journals (Sweden)

Vujošević-Janičić Milena

2009-01-01

Full Text Available In this paper we have discussed the application of the Simplex method in checking software safety - the application in automated detection of buffer overflows in C programs. This problem is important because buffer overflows are suitable targets for hackers' security attacks and sources of serious program misbehavior. We have also described our implementation, including a system for generating software correctness conditions and a Simplex based theorem prover that resolves these conditions.

ModelPlex: Verified Runtime Validation of Verified Cyber-Physical System Models

Science.gov (United States)

2014-07-01

adaptive cruise control [18], intelligent speed adaptation [23], the European train control system [35], and ground robot colli - sion avoidance [24...ground vehicles. In Paul Newman, Dieter Fox, and David Hsu, editors, Robotics: Science and Systems, 2013. ISBN 978-981-07-3937-9. URL http...3-540-71493- 4 37. 17 [34] André Platzer and Jan- David Quesel. KeYmaera: A hybrid theorem prover for hybrid sys- tems. In Alessandro Armando, Peter

Modeling Human Behaviour with Higher Order Logic: Insider Threats

DEFF Research Database (Denmark)

Boender, Jaap; Ivanova, Marieta Georgieva; Kammuller, Florian

2014-01-01

it to the sociological process of logical explanation. As a case study on modeling human behaviour, we present the modeling and analysis of insider threats as a Higher Order Logic theory in Isabelle/HOL. We show how each of the three step process of sociological explanation can be seen in our modeling of insider’s state......, its context within an organisation and the effects on security as outcomes of a theorem proving analysis....

Radon-Nikodym type theorem for α-completely positive maps

International Nuclear Information System (INIS)

Heo, Jaeseong; Ji, Un Cig

2010-01-01

We introduce a new notion of α-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between α-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure α-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant α-completely positive map (see Theorem 4.3).

On Pythagoras Theorem for Products of Spectral Triples

OpenAIRE

D'Andrea, Francesco; Martinetti, Pierre

2013-01-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...

Pauli and The Spin-Statistics Theorem

International Nuclear Information System (INIS)

Duck, Ian; Sudarshan, E.C.G.

1998-03-01

This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others

The Pythagoras' Theorem

OpenAIRE

Saikia, Manjil P.

2013-01-01

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.

Cantor's Little Theorem

Indian Academy of Sciences (India)

eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.

Double soft theorem for perturbative gravity

OpenAIRE

Saha, Arnab

2016-01-01

Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

A Converse of Fermat's Little Theorem

Science.gov (United States)

Bruckman, P. S.

2007-01-01

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

A Metrized Duality Theorem for Markov Processes

DEFF Research Database (Denmark)

Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

2014-01-01

We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

Generalized optical theorems

International Nuclear Information System (INIS)

Cahill, K.

1975-11-01

Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr

Green's Theorem for Sign Data

OpenAIRE

Houston, Louis M.

2012-01-01

Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...

A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

Institute of Scientific and Technical Information of China (English)

程立新; 腾岩梅

2003-01-01

This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

Liouville's theorem and phase-space cooling

International Nuclear Information System (INIS)

Mills, R.L.; Sessler, A.M.

1993-01-01

A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur

A primer on Higgs boson low-energy theorems

International Nuclear Information System (INIS)

Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA

1989-05-01

We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs

DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM

OpenAIRE

Sato, Junichi; Kawasaki, Hidefumi

2007-01-01

Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.

Notes on the area theorem

International Nuclear Information System (INIS)

Park, Mu-In

2008-01-01

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons

Optimal no-go theorem on hidden-variable predictions of effect expectations

Science.gov (United States)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

The Classical Version of Stokes' Theorem Revisited

Science.gov (United States)

Markvorsen, Steen

2008-01-01

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

The divergence theorem for unbounded vector fields

OpenAIRE

De Pauw, Thierry; Pfeffer, Washek F.

2007-01-01

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.

Gleason-Busch theorem for sequential measurements

Science.gov (United States)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

The relativistic virial theorem

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.

1989-11-01

The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

The large deviations theorem and ergodicity

International Nuclear Information System (INIS)

Gu Rongbao

2007-01-01

In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions

Gödel's Theorem

NARCIS (Netherlands)

Dalen, D. van

The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next

Visualizing the Central Limit Theorem through Simulation

Science.gov (United States)

Ruggieri, Eric

2016-01-01

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

The equivalence theorem

International Nuclear Information System (INIS)

Veltman, H.

1990-01-01

The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs

Towards the Formal Verification of a Distributed Real-Time Automotive System

Science.gov (United States)

Endres, Erik; Mueller, Christian; Shadrin, Andrey; Tverdyshev, Sergey

2010-01-01

We present the status of a project which aims at building, formally and pervasively verifying a distributed automotive system. The target system is a gate-level model which consists of several interconnected electronic control units with independent clocks. This model is verified against the specification as seen by a system programmer. The automotive system is implemented on several FPGA boards. The pervasive verification is carried out using combination of interactive theorem proving (Isabelle/HOL) and model checking (LTL).

Out-of-time-order fluctuation-dissipation theorem

Science.gov (United States)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Scale symmetry and virial theorem

International Nuclear Information System (INIS)

Westenholz, C. von

1978-01-01

Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework

On Pythagoras Theorem for Products of Spectral Triples

Science.gov (United States)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Convergence theorems for certain classes of nonlinear mappings

International Nuclear Information System (INIS)

Chidume, C.E.

1992-01-01

Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs

Markov's theorem and algorithmically non-recognizable combinatorial manifolds

International Nuclear Information System (INIS)

Shtan'ko, M A

2004-01-01

We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem

A note on the weighted Khintchine-Groshev Theorem

DEFF Research Database (Denmark)

Hussain, Mumtaz; Yusupova, Tatiana

Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

Science.gov (United States)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

A Hohenberg-Kohn theorem for non-local potentials

International Nuclear Information System (INIS)

Meron, E.; Katriel, J.

1977-01-01

It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)

Non-renormalisation theorems in string theory

International Nuclear Information System (INIS)

Vanhove, P.

2007-10-01

In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)

Singularity theorems from weakened energy conditions

International Nuclear Information System (INIS)

Fewster, Christopher J; Galloway, Gregory J

2011-01-01

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

燕居让

1991-01-01

We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.

Integrable equations, addition theorems, and the Riemann-Schottky problem

International Nuclear Information System (INIS)

Buchstaber, Viktor M; Krichever, I M

2006-01-01

The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

The Weinberg-Witten theorem on massless particles: an essay

International Nuclear Information System (INIS)

Loebbert, F.

2008-01-01

In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

Theorems of low energy in Compton scattering

International Nuclear Information System (INIS)

Chahine, J.

1984-01-01

We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt

Zamolodchikov's c-theorem and string effective actions

International Nuclear Information System (INIS)

Mavromatos, N.E.; Miramontes, J.L.

1988-01-01

Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)

There is No Quantum Regression Theorem

International Nuclear Information System (INIS)

Ford, G.W.; OConnell, R.F.

1996-01-01

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society

Adiabatic Theorem for Quantum Spin Systems

Science.gov (United States)

Bachmann, S.; De Roeck, W.; Fraas, M.

2017-08-01

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

Theorem Proving In Higher Order Logics

Science.gov (United States)

Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene

2002-01-01

The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

Soft theorems from conformal field theory

International Nuclear Information System (INIS)

Lipstein, Arthur E.

2015-01-01

Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.

The Surprise Examination Paradox and the Second Incompleteness Theorem

OpenAIRE

Kritchman, Shira; Raz, Ran

2010-01-01

We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...

COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.

Generalizations of the Nash Equilibrium Theorem in the KKM Theory

Directory of Open Access Journals (Sweden)

Sehie Park

2010-01-01

Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.

Testing the No-Hair Theorem with Sgr A*

Directory of Open Access Journals (Sweden)

Tim Johannsen

2012-01-01

Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.

Quantization of Chirikov Map and Quantum KAM Theorem.

Science.gov (United States)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions

Cosmological constant, inflation and no-cloning theorem

Energy Technology Data Exchange (ETDEWEB)

Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)

2012-05-30

From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.

Elastic hadron scattering and optical theorem

CERN Document Server

Lokajicek, Milos V.; Prochazka, Jiri

2014-01-01

In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.

Two fixed point theorems on quasi-metric spaces via mw- distances

Energy Technology Data Exchange (ETDEWEB)

Alegre, C.

2017-07-01

In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)

On the Riesz representation theorem and integral operators ...

African Journals Online (AJOL)

We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...

A generalization of the virial theorem for strongly singular potentials

International Nuclear Information System (INIS)

Gesztesy, F.; Pittner, L.

1978-09-01

Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)

Wigner's Symmetry Representation Theorem

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...

Logic for computer science foundations of automatic theorem proving

CERN Document Server

Gallier, Jean H

2015-01-01

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir

Quantum voting and violation of Arrow's impossibility theorem

Science.gov (United States)

Bao, Ning; Yunger Halpern, Nicole

2017-06-01

We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

2013-01-01

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

Goedel incompleteness theorems and the limits of their applicability. I

International Nuclear Information System (INIS)

Beklemishev, Lev D

2011-01-01

This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

Goedel incompleteness theorems and the limits of their applicability. I

Energy Technology Data Exchange (ETDEWEB)

Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2011-01-25

This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

H-theorem in quantum physics.

Science.gov (United States)

Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

Leaning on Socrates to Derive the Pythagorean Theorem

Science.gov (United States)

Percy, Andrew; Carr, Alistair

2010-01-01

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

Four theorems on the psychometric function.

Science.gov (United States)

May, Keith A; Solomon, Joshua A

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

Four theorems on the psychometric function.

Directory of Open Access Journals (Sweden)

Keith A May

Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is

On the Leray-Hirsch Theorem for the Lichnerowicz cohomology

International Nuclear Information System (INIS)

Ait Haddoul, Hassan

2004-03-01

The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)

A Note on a Broken-Cycle Theorem for Hypergraphs

Directory of Open Access Journals (Sweden)

Trinks Martin

2014-08-01

Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there

Kochen-Specker theorem studied with neutron interferometer.

Science.gov (United States)

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Kochen-Specker theorem studied with neutron interferometer

Energy Technology Data Exchange (ETDEWEB)

Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

A note on the homomorphism theorem for hemirings

Directory of Open Access Journals (Sweden)

D. M. Olson

1978-01-01

Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.

Converse Barrier Certificate Theorems

DEFF Research Database (Denmark)

Wisniewski, Rafael; Sloth, Christoffer

2016-01-01

This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...

Direct and converse theorems the elements of symbolic logic

CERN Document Server

Gradshtein, I S; Stark, M; Ulam, S

1963-01-01

Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap

Level comparison theorems and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Baumgartner, B.; Grosse, H.

1986-01-01

The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)

Generalized Panofsky-Wenzel theorem and hybrid coupling

CERN Document Server

Smirnov, A V

2001-01-01

The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.

Joint probability distributions and fluctuation theorems

International Nuclear Information System (INIS)

García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

2012-01-01

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators

Fully Quantum Fluctuation Theorems

Science.gov (United States)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Deviations from Wick's theorem in the canonical ensemble

Science.gov (United States)

Schönhammer, K.

2017-07-01

Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.

Action-angle variables and a KAM theorem for b-Poisson manifolds

OpenAIRE

Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

2015-01-01

In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

A new proof of the positive energy theorem

International Nuclear Information System (INIS)

Witten, E.

1981-01-01

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)

Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions

Science.gov (United States)

Yang, Chuan-Fu

Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.

Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems

OpenAIRE

Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor

2013-01-01

Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...

The low-energy theorem of pion photoproduction using the Skyrme model

International Nuclear Information System (INIS)

Ikehashi, T.; Ohta, K.

1995-01-01

We reassess the validity of the current-algebra based low-energy theorem of pion photoproduction on the nucleon using the Skyrme model. We find that one of the off-shell electromagnetic form factors of the nucleon exhibits infrared divergence in the chiral limit. This contribution introduces an additional term to the threshold amplitude predicted by the low-energy theorem. The emergence of the additional term indicates an unavoidable necessity of off-shell form factors in deriving the low-energy theorem. In the case of neutral pion production, the new contribution to the threshold amplitude is found to be comparable in magnitude to the low-energy theorem's prediction and has the opposite sign. In the charged pion production channels, the correction to the theorem is shown to be relatively small. (orig.)

Dynamic Newton-Puiseux Theorem

DEFF Research Database (Denmark)

Mannaa, Bassel; Coquand, Thierry

2013-01-01

A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...

A Maximal Element Theorem in FWC-Spaces and Its Applications

Science.gov (United States)

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Pauli and the spin-statistics theorem

CERN Document Server

Duck, Ian M

1997-01-01

This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that

Quantum nonlocality and reality 50 years of Bell's theorem

CERN Document Server

Gao, Shan

2016-01-01

Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...

On the c-theorem in higher genus

International Nuclear Information System (INIS)

Espriu, D.; Mavromatos, N.E.

1990-01-01

We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)

The Hellman-Feynman theorem at finite temperature

International Nuclear Information System (INIS)

Cabrera, A.; Calles, A.

1990-01-01

The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

Kochen-Specker theorem studied with neutron interferometer

International Nuclear Information System (INIS)

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-01-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Strong converse theorems using Rényi entropies

Energy Technology Data Exchange (ETDEWEB)

Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

2016-08-15

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Guided Discovery of the Nine-Point Circle Theorem and Its Proof

Science.gov (United States)

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

An extension of Brosowski-Meinardus theorem on invariant approximation

International Nuclear Information System (INIS)

Liaqat Ali Khan; Abdul Rahim Khan.

1991-07-01

We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs

K S Krishnan's 1948 Perception of the Sampling Theorem

Indian Academy of Sciences (India)

K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...

An improved version of the Mar otto Theorem

International Nuclear Information System (INIS)

Li Changpin; Chen Guanrong

2003-01-01

In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived

A remark on the energy conditions for Hawking's area theorem

Science.gov (United States)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

OpenAIRE

Markvorsen, Steen

2006-01-01

The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...

Automatic Construction of Finite Algebras

Institute of Scientific and Technical Information of China (English)

张健

1995-01-01

This paper deals with model generation for equational theories,i.e.,automatically generating (finite)models of a given set of (logical) equations.Our method of finite model generation and a tool for automatic construction of finite algebras is described.Some examples are given to show the applications of our program.We argue that,the combination of model generators and theorem provers enables us to get a better understanding of logical theories.A brief comparison betwween our tool and other similar tools is also presented.

Matching factorization theorems with an inverse-error weighting

Science.gov (United States)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

2018-06-01

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

An arithmetic transference proof of a relative Szemer\\'edi theorem

OpenAIRE

Zhao, Yufei

2013-01-01

Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemer\\'edi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only ...

A non-renormalization theorem for conformal anomalies

International Nuclear Information System (INIS)

Petkou, Anastasios; Skenderis, Kostas

1999-01-01

We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

An ACL2 Mechanization of an Axiomatic Framework for Weak Memory

Directory of Open Access Journals (Sweden)

Benjamin Selfridge

2014-06-01

Full Text Available Proving the correctness of programs written for multiple processors is a challenging problem, due in no small part to the weaker memory guarantees afforded by most modern architectures. In particular, the existence of store buffers means that the programmer can no longer assume that writes to different locations become visible to all processors in the same order. However, all practical architectures do provide a collection of weaker guarantees about memory consistency across processors, which enable the programmer to write provably correct programs in spite of a lack of full sequential consistency. In this work, we present a mechanization in the ACL2 theorem prover of an axiomatic weak memory model (introduced by Alglave et al.. In the process, we provide a new proof of an established theorem involving these axioms.

The Boundary Crossing Theorem and the Maximal Stability Interval

Directory of Open Access Journals (Sweden)

Jorge-Antonio López-Renteria

2011-01-01

useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.

The nekhoroshev theorem and long-term stabilities in the solar system

Directory of Open Access Journals (Sweden)

Guzzo M.

2015-01-01

Full Text Available The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev’s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev’s theorem a reference stability result for many applications in the Solar System dynamics.

Correction of the closed orbit and vertical dispersion and the tuning and field correction system in ISABELLE

International Nuclear Information System (INIS)

Parzen, G.

1979-01-01

Each ring in ISABELLE will have 10 separately powered systematic field correction coils to make required corrections which are the same in corresponding magnets around the ring. These corrections include changing the ν-value, shaping the working line in ν-space, correction of field errors due to iron saturation effects, the conductor arrangements, the construction of the coil ends, diamagnetic effects in the superconductor and to rate-dependent induced currents. The twelve insertion quadrupoles in the insertion surrounding each crossing point will each have a quadrupole trim coil. The closed orbit will be controlled by a system of 84 horizontal dipole coils and 90 vertical dipole coils in each ring, each coil being separately powered. This system of dipole coils will also be used to correct the vertical dispersion at the crossing points. Two families of skew quadrupoles per ring will be provided for correction of the coupling between the horizontal and vertical motions. Although there will be 258 separately powered correction coils in each ring

A Randomized Central Limit Theorem

International Nuclear Information System (INIS)

Eliazar, Iddo; Klafter, Joseph

2010-01-01

The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.

A no-hair theorem for black holes in f(R) gravity

Science.gov (United States)

Cañate, Pedro

2018-01-01

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

International Nuclear Information System (INIS)

Stenlund, Mikko

2016-01-01

We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

Energy Technology Data Exchange (ETDEWEB)

Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)

2016-09-15

We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

Some functional limit theorems for compound Cox processes

Energy Technology Data Exchange (ETDEWEB)

Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Some functional limit theorems for compound Cox processes

International Nuclear Information System (INIS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-01-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

A short list color proof of Grotzsch's theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2000-01-01

We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....

On the information-theoretic approach to G\\"odel's incompleteness theorem

OpenAIRE

D'Abramo, Germano

2002-01-01

In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.

On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...

African Journals Online (AJOL)

... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.

Quantum de Finetti theorem in phase-space representation

International Nuclear Information System (INIS)

Leverrier, Anthony; Cerf, Nicolas J.

2009-01-01

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

Some commutativity theorems for a certain class of rings

International Nuclear Information System (INIS)

Khan, M.A.

1994-08-01

In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs

Hadronic interactions of the J/ψ and Adler's theorem

International Nuclear Information System (INIS)

Bourque, A.; Gale, C.; Haglin, K.L.

2004-01-01

Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled

Towards a Novel no-hair Theorem for Black Holes

CERN Document Server

Hertog, T

2006-01-01

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

Science.gov (United States)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

On the interpretation and relevance of the Fundamental Theorem of Natural Selection.

Science.gov (United States)

Ewens, Warren J; Lessard, Sabin

2015-09-01

The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness. In the continuous-time case the partial rate of change in mean fitness is equal to the parental generation additive genetic variance in fitness with no division by the mean fitness. This "partial change" has been interpreted by some as the change in mean fitness due to changes in gene frequency, and by others as the change in mean fitness due to natural selection. (Fisher variously used both interpretations.) In this paper we discuss these interpretations of the theorem. We indicate why we are unhappy with both. We also discuss the long-term relevance of the Fundamental Theorem of Natural Selection, again reaching a negative assessment. We introduce and discuss the concept of genic evolutionary potential. We finally review an optimizing theorem that involves changes in gene frequency, the additive genetic variance in fitness and the mean fitness itself, all of which are involved in the Fundamental Theorem of Natural Selection, and which is free of the difficulties in interpretation of the Fundamental Theorem of Natural Selection. Copyright © 2015 Elsevier Inc. All rights reserved.

The universality of the Carnot theorem

International Nuclear Information System (INIS)

Gonzalez-Ayala, Julian; Angulo-Brown, F

2013-01-01

It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)

Opechowski's theorem and commutator groups

International Nuclear Information System (INIS)

Caride, A.O.; Zanette, S.I.

1985-01-01

It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt

Generalized Fourier slice theorem for cone-beam image reconstruction.

Science.gov (United States)

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Kolmogorov-Arnold-Moser Theorem

Indian Academy of Sciences (India)

system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...

Limit theorems for stationary increments Lévy driven moving averages

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas; Lachièze-Rey, Raphaël; Podolskij, Mark

of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem...

Probability densities and the radon variable transformation theorem

International Nuclear Information System (INIS)

Ramshaw, J.D.

1985-01-01

D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation

Quantum work fluctuation theorem: Nonergodic Brownian motion case

International Nuclear Information System (INIS)

Bai, Zhan-Wu

2014-01-01

The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

Noncommutative gauge field theories: A no-go theorem

International Nuclear Information System (INIS)

Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

2001-06-01

Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)

Fluctuation theorems and atypical trajectories

International Nuclear Information System (INIS)

Sahoo, M; Lahiri, S; Jayannavar, A M

2011-01-01

In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.

A uniform Tauberian theorem in dynamic games

Science.gov (United States)

Khlopin, D. V.

2018-01-01

Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.

The aftermath of the intermediate value theorem

Directory of Open Access Journals (Sweden)

Morales Claudio H

2004-01-01

Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.

At math meetings, enormous theorem eclipses fermat.

Science.gov (United States)

Cipra, B

1995-02-10

Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.

A general conservative extension theorem in process algebras with inequalities

NARCIS (Netherlands)

d' Argenio, P.R.; Verhoef, Chris

1997-01-01

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to

Capacity theory with local rationality the strong Fekete-Szegö theorem on curves

CERN Document Server

Rumely, Robert

2013-01-01

This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if [a,b] is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both alg...

A Geometrical Approach to Bell's Theorem

Science.gov (United States)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

A Meinardus Theorem with Multiple Singularities

Science.gov (United States)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions

Directory of Open Access Journals (Sweden)

Tomás Pérez Becerra

2018-01-01

Full Text Available Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.

An Application of Automated Theorem Provers to Computer System Security: The Schematic Protection Model

Science.gov (United States)

2010-06-01

z ∃ dom(Y) • true A link is denoted by a function linki (X, Y) where X and Y are formal parameters representing entities and is evaluated as true or...X/rc ∃ dom(Y), • linki (Y, Z), and • τ(X)/r:c ∃ fi(τ(Y), τ(Z)). The addition of the filter, made possible by the protection types, distinguishes the

Shell theorem for spontaneous emission

DEFF Research Database (Denmark)

Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter

2013-01-01

and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....

General H-theorem and Entropies that Violate the Second Law

Directory of Open Access Journals (Sweden)

Alexander N. Gorban

2014-04-01

Full Text Available H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma. Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy. Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation. A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions Ai ⇌ Aj . This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.

Metrical theorems on systems of small inhomogeneous linear forms

DEFF Research Database (Denmark)

Hussain, Mumtaz; Kristensen, Simon

In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....

A generalization of Abel's Theorem and the Abel-Jacobi map

DEFF Research Database (Denmark)

Dupont, Johan Louis; Kamber, Franz W.

We generalize Abel’s classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold Md ⊂ Xn in a compact oriented Riemannian n–manifold, or more generally for any d–cycle Z relative to a triangulation of X, we define a (simplicial) (n − d − 1)–gerbe Z......, the Abel gerbe determined by Z, whose vanishing as a Deligne cohomology class generalizes the notion of ‘linear equivalence to zero’. In this setting, Abel’s theorem remains valid. Moreover, we generalize the classical Inversion Theorem for the Abel–Jacobi map, thereby proving that the moduli space of Abel...

Assertion checking environment (ACE) for formal verification of C programs

International Nuclear Information System (INIS)

Sharma, Babita; Dhodapkar, S.D.; Ramesh, S.

2003-01-01

In this paper we describe an Assertion Checking Environment (ACE) for compositional verification of programs, which are written in an industrially sponsored safe subset of C programming language called MISRA C [Guidelines for the Use of the C Language in Vehicle Based Software, 1998]. The theory is based on Hoare logic [Commun. ACM 12 (1969) 576] and the C programs are verified using static assertion checking technique. First the functional specifications of the program, captured in the form of pre- and post-conditions for each C function, are derived from the specifications. These pre- and post-conditions are then introduced as assertions (also called annotations or formal comments) in the program code. The assertions are then proved formally using ACE and theorem proving tool called Stanford Temporal Prover [The Stanford Temporal Prover User's Manual, 1998]. ACE has been developed by us and consists mainly of a translator c2spl, a GUI and some utility programs. The technique and tools developed are targeted towards verification of real-time embedded software

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

Science.gov (United States)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

Fourier diffraction theorem for diffusion-based thermal tomography

International Nuclear Information System (INIS)

Baddour, Natalie

2006-01-01

There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging

Is the Quantum State Real? An Extended Review of ψ-ontology Theorems

Directory of Open Access Journals (Sweden)

Matthew Saul Leifer

2014-11-01

Full Text Available Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge; Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

Science.gov (United States)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Bell's theorem, accountability and nonlocality

International Nuclear Information System (INIS)

Vona, Nicola; Liang, Yeong-Cherng

2014-01-01

Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

Science.gov (United States)

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Bayes' theorem and its application to nuclear power plant safety

International Nuclear Information System (INIS)

Matsuoka, Takeshi

2013-01-01

Bayes' theorem has been paid in much attention for its application to Probabilistic Safety Assessment (PSA). In this lecture, the basis for understanding Bayes' theorem is first explained and how to interpret the Bayes' equation with respect to the pair of conjugate distributions between prior distribution and likelihood. Then for the application to PSA, component failure data are evaluated by Bayes' theorem by using the examples of demand probability of the start of diesel generator and failure of pressure sensor. Frequencies of nuclear power plant accidents are also evaluated by Bayes' theorem for the example case of frequency of 'fires in reactor compartment' and 'core melt' frequency with the experience of Fukushima dai-ichi accidents. Lastly, several contrasting arguments are introduced briefly between favorable and critical peoples regarding the Bayes' methods. (author)

Non-renormalization theorems andN=2 supersymmetric backgrounds

International Nuclear Information System (INIS)

Butter, Daniel; Wit, Bernard de; Lodato, Ivano

2014-01-01

The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed

Twelve years before the quantum no-cloning theorem

Science.gov (United States)

Ortigoso, Juan

2018-03-01

The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.

Strong limit theorems in noncommutative L2-spaces

CERN Document Server

Jajte, Ryszard

1991-01-01

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

A power counting theorem for Feynman integrals on the lattice

International Nuclear Information System (INIS)

Reisz, T.

1988-01-01

A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)

Differentiation of retarded integrals and the divergence theorem for retarded functions with discontinuities

International Nuclear Information System (INIS)

Cooperstock, F.I.; Lim, P.H.

1986-01-01

Theorems expressing the time derivatives of retarded volume and surface integrals are presented as well as the Gauss divergence theorem for retarded functions with discontinuities. These theorems greatly facilitate the analysis of gravitational radiation from the motion of disjoint matter distributions in general relativity and could find useful application in other branches of physics

Multivariable Chinese Remainder Theorem

Indian Academy of Sciences (India)

IAS Admin

to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...

Angle Defect and Descartes' Theorem

Science.gov (United States)

Scott, Paul

2006-01-01

Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)

Optical theorem and its history

International Nuclear Information System (INIS)

Newton, R.G.

1978-01-01

A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)

Goedel's theorem and leapfrog

International Nuclear Information System (INIS)

Lloyd, Mark Anthony

1999-01-01

We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us

Expanding the Interaction Equivalency Theorem

Directory of Open Access Journals (Sweden)

Brenda Cecilia Padilla Rodriguez

2015-06-01

Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.

Radon transformation on reductive symmetric spaces:Support theorems

DEFF Research Database (Denmark)

Kuit, Job Jacob

2013-01-01

We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....

Convergence theorems for Banach space valued integrable multifunctions

Directory of Open Access Journals (Sweden)

Nikolaos S. Papageorgiou

1987-01-01

Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

Poisson's theorem and integrals of KdV equation

International Nuclear Information System (INIS)

Tasso, H.

1978-01-01

Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)

Extension and reconstruction theorems for the Urysohn universal metric space

Czech Academy of Sciences Publication Activity Database

Kubiś, Wieslaw; Rubin, M.

2010-01-01

Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544

On the Fourier integral theorem

NARCIS (Netherlands)

Koekoek, J.

1987-01-01

Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the

A New Simple Approach for Entropy and Carnot Theorem

International Nuclear Information System (INIS)

Veliev, E. V.

2004-01-01

Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem

H-theorems from macroscopic autonomous equations

Czech Academy of Sciences Publication Activity Database

De Roeck, W.; Maes, C.; Netočný, Karel

2006-01-01

Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006

Differentiability in density-functional theory: Further study of the locality theorem

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2004-01-01

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

Science.gov (United States)

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

Asymptotic twistor theory and the Kerr theorem

International Nuclear Information System (INIS)

Newman, Ezra T

2006-01-01

We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

Proofs and generalizations of the pythagorean theorem

Directory of Open Access Journals (Sweden)

Lialda B. Cavalcanti

2011-01-01

Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.

KLN theorem and infinite statistics

International Nuclear Information System (INIS)

Grandou, T.

1992-01-01

The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs

Fermion fractionization and index theorem

International Nuclear Information System (INIS)

Hirayama, Minoru; Torii, Tatsuo

1982-01-01

The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

The Geometric Mean Value Theorem

Science.gov (United States)

de Camargo, André Pierro

2018-01-01

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Science.gov (United States)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case

Energy Technology Data Exchange (ETDEWEB)

Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.

2010-08-29

Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.

A general product measurability theorem with applications to variational inequalities

Directory of Open Access Journals (Sweden)

Kenneth L. Kuttler

2016-03-01

Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.

Fixed-point theorems for families of weakly non-expansive maps

Science.gov (United States)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)

2015-11-15

We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A Short Proof of Klee's Theorem

OpenAIRE

Zanazzi, John J.

2013-01-01

In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.

A Density Turán Theorem

Czech Academy of Sciences Publication Activity Database

Narins, L.; Tran, Tuan

2017-01-01

Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016

The Completeness Theorem of Godel

Indian Academy of Sciences (India)

GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...

On the Stone-Weierstrass theorem for scalar and vector valued functions

International Nuclear Information System (INIS)

Khan, L.A.

1991-09-01

In this paper we discuss the formulation of the Stone-Weierstrass approximation theorem for vector-valued functions and then determine whether the classical Stone-Weierstrass theorem for scalar-valued functions can be deduced from the above one. We also state some open problems in this area. (author). 15 refs

There's Something About Gödel The Complete Guide to the Incompleteness Theorem

CERN Document Server

Berto, Francesco

2009-01-01

Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments.Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chaptersDiscusses interpretations of the Theorem made by celebrated contemporary thinkersSheds light on the wider extra-mathematical and philosophical implications of Gödel's theoriesWritten in an accessible, non-technical style

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

Energy Technology Data Exchange (ETDEWEB)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com [Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it [Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano (Italy)

2016-02-15

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion of spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.

A variational proof of Thomson's theorem

Energy Technology Data Exchange (ETDEWEB)

Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)

2016-08-12

Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.

Vanishing theorems and effective results in algebraic geometry

International Nuclear Information System (INIS)

Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.

2001-01-01

The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks

Refinement of Representation Theorems for Context-Free Languages

Science.gov (United States)

Fujioka, Kaoru

In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.

Vanishing theorems and effective results in algebraic geometry

Energy Technology Data Exchange (ETDEWEB)

Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)

2001-12-15

The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.

Theorem on axially symmetric gravitational vacuum configurations

Energy Technology Data Exchange (ETDEWEB)

Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare

1977-01-24

A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.

On Nonlinear Prices in Timed Automata

Directory of Open Access Journals (Sweden)

Devendra Bhave

2016-12-01

Full Text Available Priced timed automata provide a natural model for quantitative analysis of real-time systems and have been successfully applied in various scheduling and planning problems. The optimal reachability problem for linearly-priced timed automata is known to be PSPACE-complete. In this paper we investigate priced timed automata with more general prices and show that in the most general setting the optimal reachability problem is undecidable. We adapt and implement the construction of Audemard, Cimatti, Kornilowicz, and Sebastiani for non-linear priced timed automata using state-of-the-art theorem prover Z3 and present some preliminary results.

Specifying and Verifying Organizational Security Properties in First-Order Logic

Science.gov (United States)

Brandt, Christoph; Otten, Jens; Kreitz, Christoph; Bibel, Wolfgang

In certain critical cases the data flow between business departments in banking organizations has to respect security policies known as Chinese Wall or Bell-La Padula. We show that these policies can be represented by formal requirements and constraints in first-order logic. By additionally providing a formal model for the flow of data between business departments we demonstrate how security policies can be applied to a concrete organizational setting and checked with a first-order theorem prover. Our approach can be applied without requiring a deep formal expertise and it therefore promises a high potential of usability in the business.

A Paraconsistent Higher Order Logic

DEFF Research Database (Denmark)

Villadsen, Jørgen

2004-01-01

of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order...... of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens. Many non-classical logics are, at the propositional level, funny toys which work quite good, but when one wants...

Feasibility study of experiments to measure inclusive reactions at large x/sub F/ in ISABELLE's small-angle hall

International Nuclear Information System (INIS)

Aronson, S.; Danby, G.; Foley, K.; Paige, F.; Thorndike, A.; Engelmann, R.; McCarthy, R.; Pope, B.

1978-01-01

As a way of testing current ideas on the construction of experimental halls at ISABELLE, a particular class of experiments suggested for the small-angle (or 2 o' clock) hall, p + p → p + X and p + p → c + X, c not equal to p is examined. The result of this examination is that inclusive single-particle experiments are feasible over a suitable kinematic range without the use of previously proposed special insertion quadrupoles. The forward single-arm spectrometer is housed in a separate tunnel of modest transverse dimension. The extraction of scattered particles (theta greater than or equal to 1 mrad) into the spectrometer is accomplished with Lambertson septa and current sheet septa. Provision is made for overlap with the kinematic region covered by ISR and Fermilab experiments. The physics objectives of such experiments are reviewed first. Then the general layout of the apparatus is described, with special emphasis on the extraction system and the spectrometer. A guess at how this experiment would fit into the overall small-angle physics program is presented. 5 figures

Nash-Williams’ cycle-decomposition theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2016-01-01

We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...

ON A LAGUERRE’S THEOREM

Directory of Open Access Journals (Sweden)

SEVER ANGEL POPESCU

2015-03-01

Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:

Lagrange’s Four-Square Theorem

Directory of Open Access Journals (Sweden)

Watase Yasushige

2015-02-01

Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].

A THEOREM ON CENTRAL VELOCITY DISPERSIONS

International Nuclear Information System (INIS)

An, Jin H.; Evans, N. Wyn

2009-01-01

It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.

The g-theorem and quantum information theory

Energy Technology Data Exchange (ETDEWEB)

Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)

2016-10-25

We study boundary renormalization group flows between boundary conformal field theories in 1+1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

The Pi-Theorem Applications to Fluid Mechanics and Heat and Mass Transfer

CERN Document Server

Yarin, L P

2012-01-01

This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.

Acceleration theorems

International Nuclear Information System (INIS)

Palmer, R.

1994-06-01

Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation

Limit theorems for multi-indexed sums of random variables

CERN Document Server

Klesov, Oleg

2014-01-01

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...

More on Weinberg's no-go theorem in quantum gravity

Science.gov (United States)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Locally Hamiltonian systems with symmetry and a generalized Noether's theorem

International Nuclear Information System (INIS)

Carinena, J.F.; Ibort, L.A.

1985-01-01

An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective

A short list color proof of Grötzsch's theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2003-01-01

We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable.......We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable....

Relaxed Bell inequalities and Kochen-Specker theorems

Energy Technology Data Exchange (ETDEWEB)

Hall, Michael J. W. [Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)

2011-08-15

The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet-state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various ''relaxed'' Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen ''free will'' theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows that existence of an outcome-independent model is equivalent to existence of a deterministic model.

Two theorems on flat space-time gravitational theories

International Nuclear Information System (INIS)

Castagnino, M.; Chimento, L.

1980-01-01

The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)

Restriction Theorem for Principal bundles in Arbitrary Characteristic

DEFF Research Database (Denmark)

Gurjar, Sudarshan

2015-01-01

The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...

Real representations of Lie groups and a theorem of H. Pittie

International Nuclear Information System (INIS)

Freitas, R.

1992-01-01

In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs

Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

Science.gov (United States)

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

A common fixed point theorem for weakly compatible mappings in Menger probabilistic quasi metric space

Directory of Open Access Journals (Sweden)

Badridatt Pant

2014-02-01

Full Text Available In this paper, we prove a common fixed point theorem for finite number of self mappings in Menger probabilistic quasi metric space. Our result improves and extends the results of Rezaiyan et al. [A common fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 37 (2008 1153-1157.], Miheţ [A note on a fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 40 (2009 2349-2352], Pant and Chauhan [Fixed points theorems in Menger probabilistic quasi metric spaces using weak compatibility, Internat. Math. Forum 5 (6 (2010 283-290] and Sastry et al. [A fixed point theorem in Menger PQM-spaces using weak compatibility, Internat. Math. Forum 5 (52 (2010 2563-2568

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

Science.gov (United States)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Green-Tao theorem in function fields

OpenAIRE

Le, Thai Hoang

2009-01-01

We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)

On the extension of the Fermi-Watson Theorem to high energy diffraction

International Nuclear Information System (INIS)

Malecki, A.; Istituto Nazionale di Fisica Nucleare, Frascati

1995-12-01

The Fermi-Watson theorem, established for low energy reactions and then applied to high energy collision, is revisited. Its use for the processes of inelastic diffraction is discussed. The theorem turns out to be valid in the case inclusive cross-section of diffractive transition

Supersymmetric extension of the Adler-Bardeen theorem

International Nuclear Information System (INIS)

Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.

1985-01-01

A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)

Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

International Nuclear Information System (INIS)

Ensign, P.W.

1987-01-01

By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem

An existence theorem for a type of functional differential equation with infinite delay

NARCIS (Netherlands)

Izsak, F.

We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.

Confusion and Clarification: Albert Einstein and Walther Nernst's Heat Theorem, 1911-1916

NARCIS (Netherlands)

Kox, A.J.

2006-01-01

This paper discusses the early history of Walther Nernst's Heat Theorem and the first stages of its development into the Third Law of Thermodynamics. In addition to published papers, informal discussions were important in shaping the understanding of the meaning and validity of the Theorem. Special

Quantum and classical strong direct product theorems and optimal time-space tradeoffs

NARCIS (Netherlands)

H. Klauck (Hartmut); R. Spalek (Robert); R. M. de Wolf (Ronald)

2007-01-01

textabstractA strong direct product theorem says that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then our overall success probability will be exponentially small in $k$. We establish such theorems for the

A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem

International Nuclear Information System (INIS)

Prykarpatsky, A.K.

2007-05-01

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)

1/4-pinched contact sphere theorem

DEFF Research Database (Denmark)

Ge, Jian; Huang, Yang

2016-01-01

Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)

A DIDACTIC SURVEY OVER MAIN CHARACTERISTICS OF LAGRANGE'S THEOREM IN MATHEMATICS AND IN ECONOMICS

OpenAIRE

Xhonneux, Sebastian; Henry, Valérie

2011-01-01

Because of its many uses, the constrained optimization problem is presented in most calculus courses for mathematicians but also for economists. Looking at Lagrange's Theorem we are interested in studying the teaching of this theorem in both branches of study, mathematics and economics. This paper faces a twofold objective: first, we show the methodology of our research project concerning the didactic transposition of Lagrange's Theorem in university mathematics courses. Sec...

State-Independent Proof of Kochen—Specker Theorem with Thirty Rank-Two Projectors

International Nuclear Information System (INIS)

Toh, S. P.

2013-01-01

The Kochen—Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state-independent proof of the Kochen—Specker theorem using the smallest number of projectors, i.e., thirty rank-2 projectors, associated with the Mermin pentagram for a three-qubit system

Strong-Weak CP Hierarchy from Non-Renormalization Theorems

Energy Technology Data Exchange (ETDEWEB)

Hiller, Gudrun

2002-01-28

We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.

Entanglement, space-time and the Mayer-Vietoris theorem

Science.gov (United States)

Patrascu, Andrei T.

2017-06-01

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

On a theorem of Faltings on formal functions

Directory of Open Access Journals (Sweden)

Paola Bonacini

2007-12-01

Full Text Available In 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic. Let Y be a closed subvariety of a projective irreduciblevariety X defined over k. Assume that X ⊂ P^n , dim(X = d > 2 and Yis the intersection of X with r hyperplanes of P^n , with r ≤ d − 1. Then,every formal rational function on X along Y can be (uniquely extended toa rational function on X . Due to its importance, the aim of this paper is toprovide two elementary global geometric proofs of this theorem.

Modern Thermodynamics Based on the Extended Carnot Theorem

CERN Document Server

Wang, Jitao

2012-01-01

"Modern Thermodynamics- Based on the Extended Carnot Theorem" provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many "abnormal phenomena", such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China.

Double soft theorems in gauge and string theories

Energy Technology Data Exchange (ETDEWEB)

Volovich, Anastasia [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 00133 Roma (Italy); Zlotnikov, Michael [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States)

2015-07-20

We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any α{sup ′} corrections.

Belle de Zuylen / Isabelle de Charrière et l’incrédulité. De la correspondance à la fiction

Directory of Open Access Journals (Sweden)

Laurence Vanoflen

2009-04-01

Full Text Available Existe-t-il une incrédulité pensable et dicible pour une femme de milieu cultivé, au siècle des Lumières ? C’est la question que soulève la correspondance, puis la fiction d’Isabelle de Charrière (1740-1805. Vers 1764, la jeune fille de l’aristocratie hollandaise fait l’expérience des difficultés et des limites de la liberté intellectuelle, et de l’exercice de sa raison face au puritain John Boswell, puis à son compatriote Van Pallandt. Dans ses fictions et sa correspondance ultérieures, elle prend de plus en plus de recul vis-à-vis de dogmes religieux ou de convictions dont elle n’est plus bien sûre, d’ailleurs, qu’ils influent sur les conduites. Sans pour autant réhabiliter la « femme esprit fort » dans son roman Caliste (1785, comme le l’affirme C. Cazenobe, la femme mûre s’approche de plus en plus d’un nécessitarisme à relents matérialistes, avec pour seul bémol l’affirmation du pouvoir instructif de l’expérienceIncredulity is not an easy or evident posture for a woman, even in the middle of the eighteenth century. This is what Isabelle de Charrière’s (1740-1805 correspondence and fiction suggest. Towards 1764, the young woman, raised in Dutch aristocracy, tested the gender boundaries of intellectual freedom and the exercise of reason, in matter of religion. She preferred pyrrhonism to the reputation of an « esprit fort », be it with regards to the Puritain James Boswell, her fellow countryman Adolf van Pallandt, or Constant d’Hermenches. This is underlined by what we learned from the recent publication of inedits by Kees van Strien. She takes greater distance from protestant dogmas and religious convictions after 1784 when she became a novelist. While she does not quite rehabilitate the woman’s « esprit fort » in her novel Calista (1785, as C. Cazenobe asserts, her letters show how she is quite close to materialist views about human freedom, even though the lessons of

The BRST quantization and the no-ghost theorem for AdS3

International Nuclear Information System (INIS)

Asano, Masako; Natsuume, Makoto

2003-01-01

In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)

Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces

Directory of Open Access Journals (Sweden)

Sunny Chauhan

2013-05-01

Full Text Available The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3 (2010, 3-12 MR2735558].

A divergence theorem for pseudo-Finsler spaces

OpenAIRE

Minguzzi, E.

2015-01-01

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.

Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

International Nuclear Information System (INIS)

Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

2005-08-01

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

Dispersive approach to the axial anomaly and nonrenormalization theorem

International Nuclear Information System (INIS)

Pasechnik, R.S.; Teryaev, O.V.

2006-01-01

Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop

Testing subleading multiple soft graviton theorem for CHY prescription

Science.gov (United States)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

A generalized integral fluctuation theorem for general jump processes

International Nuclear Information System (INIS)

Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang

2009-01-01

Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)

Reciprocity theorem in high-temperature superconductors

Czech Academy of Sciences Publication Activity Database

Janeček, I.; Vašek, Petr

2003-01-01

Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003

On the first case of Fermat's theorem for cyclotomic fields

International Nuclear Information System (INIS)

Kolyvagin, V A

1999-01-01

The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2

Pythagoras Theorem and Relativistic Kinematics

Science.gov (United States)

Mulaj, Zenun; Dhoqina, Polikron

2010-01-01

In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.

Lectures on Fermat's last theorem

International Nuclear Information System (INIS)

Sury, B.

1993-09-01

The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT

Mean value theorem in topological vector spaces

International Nuclear Information System (INIS)

Khan, L.A.

1994-08-01

The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs

Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers

Science.gov (United States)

Bjorner, Nikolaj

2010-01-01

The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings

The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project

Science.gov (United States)

Robiette, Alan G.

1975-01-01

Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)

Student Research Project: Goursat's Other Theorem

Science.gov (United States)

Petrillo, Joseph

2009-01-01

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

Semigroups, antiautomorphisms, and involutions: A computer solution to an open problem, I

International Nuclear Information System (INIS)

Winker, S.K.; Wos, L.; Lusk, E.L.

1981-01-01

An antiautomorphism H of a semigroup S is a 1-1 mapping of S onto itself such that H(xy) = H(y)H(x) for all x,y in S. An antiautomorphism H is an involution if H 2 (x) = x for all x in S. In this paper the following question is answered: Does there exist a finite semigroup with antiautomorphism but no involution. This question, suggested by I. Kaplansky, was answered in the affirmative with the aid of an automated theorem-proving program. More precisely, there are exactly four such semigroups of order seven and none of smaller order. The program was a completely general one, and did not calculate the solution directly, but rather rendered invaluable assistance to the mathematicians investigating the question by helping to generate and examine various models. A detailed discussion of the approach is presented, with the intention of demonstrating the usefulness of a theorem prover in carrying out certain types of mathematical research

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

International Nuclear Information System (INIS)

Okabe, Y.

1985-01-01

The [α,β,γ]-Langevin equation describes the time evolution of a real stationary process with T-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [α,β,γ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics. (orig.)

Fluctuation theorem for channel-facilitated membrane transport of interacting and noninteracting solutes.

Science.gov (United States)

Berezhkovskii, Alexander M; Bezrukov, Sergey M

2008-05-15

In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.

Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

International Nuclear Information System (INIS)

Ensign, P.; Mahanthappa, K.T.

1987-01-01

We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Mills theory coupled to non-self-interacting chiral matter. Using the formulation recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory

State Prices and Implementation of the Recovery Theorem

Directory of Open Access Journals (Sweden)

Alex Backwell

2015-01-01

Full Text Available It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross [1], however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed.

Modern thermodynamics. Based on the extended Carnot theorem

Energy Technology Data Exchange (ETDEWEB)

Wang, Jitao [Fudan Univ., Shanghai (China). Microelectronics Dept.

2011-07-01

''Modern Thermodynamics- Based on the Extended Carnot Theorem'' provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many ''abnormal phenomena'', such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China. (orig.)

Fixed point theorems in locally convex spaces—the Schauder mapping method

Directory of Open Access Journals (Sweden)

S. Cobzaş

2006-03-01

Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.

On Callan's proof of the BPHZ theorem

International Nuclear Information System (INIS)

Lesniewski, A.

1984-01-01

The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)

Theorem of comparative sensitivity of fibre sensors

Science.gov (United States)

Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.

2017-12-01

We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.

Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

Directory of Open Access Journals (Sweden)

Bambang Eko Susilo

2016-03-01

Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized

Kochen-Specker theorem as a precondition for secure quantum key distribution

International Nuclear Information System (INIS)

Nagata, Koji

2005-01-01

We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory

Automata learning algorithms and processes for providing more complete systems requirements specification by scenario generation, CSP-based syntax-oriented model construction, and R2D2C system requirements transformation

Science.gov (United States)

Hinchey, Michael G. (Inventor); Margaria, Tiziana (Inventor); Rash, James L. (Inventor); Rouff, Christopher A. (Inventor); Steffen, Bernard (Inventor)

2010-01-01

Systems, methods and apparatus are provided through which in some embodiments, automata learning algorithms and techniques are implemented to generate a more complete set of scenarios for requirements based programming. More specifically, a CSP-based, syntax-oriented model construction, which requires the support of a theorem prover, is complemented by model extrapolation, via automata learning. This may support the systematic completion of the requirements, the nature of the requirement being partial, which provides focus on the most prominent scenarios. This may generalize requirement skeletons by extrapolation and may indicate by way of automatically generated traces where the requirement specification is too loose and additional information is required.

On Backward-Style Anonymity Verification

Science.gov (United States)

Kawabe, Yoshinobu; Mano, Ken; Sakurada, Hideki; Tsukada, Yasuyuki

Many Internet services and protocols should guarantee anonymity; for example, an electronic voting system should guarantee to prevent the disclosure of who voted for which candidate. To prove trace anonymity, which is an extension of the formulation of anonymity by Schneider and Sidiropoulos, this paper presents an inductive method based on backward anonymous simulations. We show that the existence of an image-finite backward anonymous simulation implies trace anonymity. We also demonstrate the anonymity verification of an e-voting protocol (the FOO protocol) with our backward anonymous simulation technique. When proving the trace anonymity, this paper employs a computer-assisted verification tool based on a theorem prover.

A non linear ergodic theorem and application to a theorem of A. Pazy

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1989-07-01

We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs

Testing ground for fluctuation theorems: The one-dimensional Ising model

Science.gov (United States)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Watson's theorem and resonant pion photoproduction amplitude in the delta channel

International Nuclear Information System (INIS)

Wittman, R.; Davidson, R.; Mukhopadhyay, N.C.

1984-01-01

The CGLN and BL theories of the pion photoproduction on nucleons, used in nuclear calculations, are examined regarding their predictions of the resonant M 1 + and E 1 + multipoles. The nonunitary BL approach violates Watson's theorem, and predicts these multipoles porly. In the static limit, the CGLN multipoles satisfy Watson's theorem and are in fine agreement with data. The unitarized BL multipoles agree with those from the Olsson theory and data. (orig.)

Thermodynamical and Green function many-body Wick theorems

International Nuclear Information System (INIS)

Westwanski, B.

1987-01-01

The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

Bell's theorem based on a generalized EPR criterion of reality

International Nuclear Information System (INIS)

Eberhard, P.H.; Rosselet, P.

1995-01-01

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future

The a theorem for Gauge-Yukawa theories beyond Banks-Zaks

DEFF Research Database (Denmark)

Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben

2013-01-01

We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the pres......We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including...

A survey of weighted substitution operators and generalizations of Banach-stone theorem

OpenAIRE

R. K. Singh

2005-01-01

The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.

Virial theorem and the Born-Oppenheimer approximation at different orders of perturbation

International Nuclear Information System (INIS)

Olivier, Gabriel; Weislinger, Edmond

1977-01-01

The link between the virial theorem and the adiabatic approximation is studied for a few orders of perturbation. It is shown that the total energy of the system is distributed between the mean values of kinetic and potential energy of the nuclei and the electrons in each order of perturbation. No static approximation connected with the Hellmann-Feynman theorem is made [fr