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In this paper we have analyzed the improved version of the Gauge Unfixing GU formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model.
In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. Save to Library. Create Alert. Launch Research Feed. Share This Paper.
References Publications referenced by this paper. Vytheeswaran J. A 13 A26 ; A. AnishettyA.Folding gun
VytheeswaranJ. Phys S. Vytheeswaran, Ann. Aghileh S. Monemzadeh Ebrahimi and S. Sramadi, Mod. A Vol. MitraR. Rajaraman Phys. Ananias Neto J. BizdadeaS. Saliu Lett. Dayi Lett. B CarrollG. FieldR. Jackiw Rev. D41 BatalinE.
Fradkin Lett. B ; I. Batalin and E.We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion OPEwithout assuming unitarity. We find the minimal models as special cases, as well as additional lines of solutions that can be understood in the Coulomb gas formalism.
All the solutions we find that contain the vacuum in the operator algebra are cases where the external operators of the bootstrap equation are degenerate operators, and we argue that this follows analytically from the expressions in arXiv In the supplementary material, we provide a Mathematica notebook that automates the calculation of the crossing matrices and OPE coefficients for degenerate operators using the formulae of Dotsenko and Fateev.
Download to read the full article text. Moore and N. Seiberg, Polynomial equations for rational conformal field theoriesPhys. Dijkgraaf, C.
Vafa, E. Verlinde and H. Verlinde, The operator algebra of orbifold modelsCommun. Lunin and S. Belavin, A. Polyakov and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theoryNucl. Liendo, L. Rastelli and B. Ribault, Conformal field theory on the planearXiv Gliozzi and A. Gliozzi, More constraining conformal bootstrapPhys. Teschner, A lecture on the Liouville vertex operatorsInt.
Ponsot and J. Teschner and G. Vartanov, 6 j symbols for the modular double, quantum hyperbolic geometry and supersymmetric gauge theoriesLett. Dotsenko and V. Fateev, Conformal algebra and multipoint correlation functions in two-dimensional statistical modelsNucl. Zamolodchikov, Conformal symmetry in two-dimensions: an explicit recurrence formula for the conformal partial wave amplitudeCommun. Zamolodchikov, Conformal symmetry in two-dimensional space: recursion representation of the conformal blockTheor.
Hartman, Entanglement entropy at large central chargearXiv Gliozzi, Truncatable bootstrap equations in algebraic form and critical surface exponentsJHEP 10 [ arXivThank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer.
For quark physics, such issues include the nature of quark confinement; the mechanism that connects the quarks and gluons of the standard model theory to the strongly interacting particles; and the weak decays of quarks, which may provide insights into new physics mechanisms responsible for the matter—antimatter asymmetry of the Universe. Measurements of the purely leptonic and semileptonic decay rates of D and D s mesons provide sensitive tests of lattice quantum chromodynamics calculations of charmed-meson decay constants and form factors.
Studies of directly produced Y mesons led to discoveries of the Z c and Z c non-standard, four-quark hadrons and a new production mode for the X Weinberg, S.
Essay: half a century of the standard model. Aubert, B. The BaBar detector. Methods A1— Abashian, A. The Belle detector. Methods A— Ablikim, M. Alves, A. Jr et al.
Gravitational waves in fourth order gravity
Do you know any efficient way since this number is too big but abcAlso please note that a b c is not the same as a b c. The later is equal to a bc. Exponentiation is right-associative. The answer does not contain full formal mathematical proof of correctness.
I assumed that it is unnecessary here. Besides, it would be very illegible on SO, no MathJax for example. I will use just a little bit specific prime factorization algorithm. It's not best option, but enough. We will use function modpow a,x,m. Described below. I will also use Euler's totient theorem.
Quoting wikipedia:. The assumption numbers are co-prime is very important, as Nabb shows in comment. So, firstly we need to ensure that the numbers are co-prime. Number has at most o log a prime factors, so we will be force to perform at most o log a calculations.
In fact we doesn't have to split to every prime factor of a if not all occur in m with other exponents and we can combine with same exponent, but it is not noteworthy by now.
Notice some important observation:. If a,b are positive integers smaller than m and c is some positive integer andthen true is sentence. Using the above observation, we can receive solution for actual problem. Now assume a,m are co-prime. Note : If some totient isn't co-prime to exponent, it is necessary to use same trick, as in main problem in fact, we should forget that it's exponent and recursively solve problem, like in main problem.
In above example, if t2 isn't relatively prime with c, we have to use this trick. Therefore we can factorize n ak. Then combine this using fact 1. It is worth remembering that, if we will calculate totient repeatedly, we may want to use Sieve of Eratosthenes and save prime numbers in table. It will reduce the constant. Cause it's in fact doing the same thing many times, I believe this case will show you how to solve this generally.
Firstly, we have to split a into prime powers. I believe I don't have to show code example to it. It's easy way to get an answer. Example below. I hope I didn't make mistake, writing. Looks, like it works. DEMO and it's correct! Edit: as Nabb pointed out, this only holds if a is coprime to m.The Federal government similarly defines indirect costs. See 2 C. LSC has learned that some LSC recipients have applied for federal, state, and local government grants, as well as private grants, using budgets that contained no or an artificially low amount for indirect costs.
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In recognition of this fact, LSC has long permitted recipients to use Basic Field Grant funds to pay for a greater amount of general operational costs than can usually be charged to federal grants. Grantees of the federal government must comply with a set of common rules applicable to all federal grants known as the Uniform Guidance. Part Many federal and non-federal grants contain terms limiting the amount of indirect costs that may be paid out of the grant.
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It cannot simply choose to allocate the entire excess balance to the Basic Field Grant without further analysis. Nor can the recipient choose to allocate the entire excess to the Basic Field Grant if it has unrestricted funds available to pay indirect costs.
Beginning inLSC became aware that some recipients have applied for private and federal grants using artificially reduced indirect cost allocations. See, e. In Report No. The language of 45 C. Rather, the rule requires a non-LSC funder to affirmatively refuse to pay the costs. Refusal to pay indirect costs may take many forms, including the following hypothetical examples:.
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I want to calculate a b mod n for use in RSA decryption. My code below returns incorrect answers. What is wrong with it? I've used it with 32 and bit integers. I'm sure I got this from SO.
Schneier, Bruce ISBN If the modulus is more than half the width of T i. Doing the raw power operation is very costly, hence you can apply the following logic to simplify the decryption. Note that we don't have to calculate the full value of 13 to the power 7 here. One way of calculating m' is as follows:- Note that any number can be expressed as a sum of powers of 2. Either way, your function is unnecessarily complex. Why not just loop until b and mulitply in one a each time.
That would eliminate a lot of unnecessary complexity and thus eliminate potential errors. Are you thinking that you'll make the program faster by cutting the number of times through the loop in half? Frankly, that's a bad programming practice: micro-optimization. It doesn't really help much: You still multiply by a the same number of times, all you do is cut down on the number of times testing the loop.
If b is typically small like one or two digitsit's not worth the trouble. If b is large -- if it can be in the millions -- then this is insufficient, you need a much more radical optimization. This is int overflow undefined behavior when a is large enough.
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There is no reason to return a wider type than the type of the modulus as the result is always represent by that type. Also see Modular exponentiation without range restriction. This encryption is more of an algorithm design problem than a programming one. The important missing part is familiarity with modern algebra. I suggest that you look for a huge optimizatin in group theory and number theory.
Therefore the range [ Given the algorithm to find e for n and logarithm of a base ecalculations can be significantly simplified. Cryptography needs a tone of math background; I'd rather be off that ground without enough background.
I parse the variable result because pow give you back a double, and for using mod you need two variables of type int, anyway, in a RSA decryption, you should just use integer numbers.
Learn more. Calculating pow a,b mod n Ask Question. Asked 8 years, 7 months ago. Active 8 months ago. Viewed 63k times. Pops In the post-Minkowskian limit approximation, we study gravitational wave solutions for general fourth-order theories of gravity.
It is well known that when dealing with General Relativity such an approach provides massless spin-two waves as propagating degree of freedom of the gravitational field while this theory implies other additional propagating modes in the gravity spectra.
Closure of the operator product expansion in the non-unitary bootstrap
We show that, in general, fourth order gravity, besides the standard massless graviton is characterized by two further massive modes with a finite-distance interaction. We find out the most general gravitational wave solutions in terms of Green functions in vacuum and in presence of matter sources.
Polarizations and helicity states are classified in the hypothesis of plane wave. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Alexander, S. Astashenok, A. D 89 Bamba, K. B Bargmann, V. USA 34 Bergmann, P. Berry, C. D 83 Bogdanos, C. Buchbinder, I. IOP Publ.Violin method pdf
Google Scholar. Capozziello, S. Quantum Gravity 26 Quantum Gravity 26a.Niacinamide and retinol reddit
Quantum Gravity 26b. D 76 A 24 9 Quantum Gravity 27a.
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