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We embed Safe Recursion on Notation (SRN) into Light Affine Logic by Levels (LALL), derived from the logic L4. LALL is an intuitionistic deductive system, with a polynomial time cut elimination strategy. The embedding allows to represent every term t of SRN as a family of proof nets |t|^l in LALL. Every proof net |t|^l in the family simulates t on arguments whose bit length is bounded by the integer l. The embedding is based on two crucial features. One is the recursive type in LALL that encodes Scott binary numerals, i.e. Scott words, as proof nets. Scott words represent the arguments of t in place of the more standard Church binary numerals. Also, the embedding exploits the "fuzzy" borders of paragraph boxes that LALL inherits from L4 to "freely" duplicate the arguments, especially the safe ones, of t. Finally, the type of |t|^l depends on the number of composition and recursion schemes used to define t, namely the structural complexity of t. Moreover, the size of |t|^l is a polynomial in l, whose degree depends on the structural complexity of t. So, this work makes closer both the predicative recursive theoretic principles SRN relies on, and the proof theoretic one, called /stratification/, at the base of Light Linear Logic.

In our previous papers \cite{doz1,doz2} we studied Laguerre functions and polynomials on symmetric cones $\Omega=H/L$. The Laguerre functions $\ell^{\nu}_{\mathbf{n}}$, $\mathbf{n}\in\mathbf{\Lambda}$, form an orthogonal basis in $L^{2}(\Omega,d\mu_{\nu})^{L}$ and are related via the Laplace transform to an orthogonal set in the representation space of a highest weight representations $(\pi_{\nu}, \mathcal{H}_{\nu})$ of the automorphism group $G$ corresponding to a tube domain $T(\Omega)$. In this article we consider the case where $\Omega$ is the space of positive definite Hermitian matrices and $G=\mathrm{SU}(n,n)$. We describe the Lie algebraic realization of $\pi_{\nu}$ acting in $L^{2}(\Omega,d\mu_{\nu})$ and use that to determine explicit differential equations and recurrence relations for the Laguerre functions.

A devil's advocate is one who argues against a claim, not as a committed opponent but in order to determine the validity of the claim. We are interested in a devil's advocate that argues against termination of a program. He does so by producing a maleficent program that can cause the non-termination of the original program. By inspecting and running the malicious program, one may gain insight into the potential reasons for non-termination and produce counterexamples for termination. We introduce our method using the concurrent programming language Constraint Handling Rules (CHR). Like in other declarative languages, non-termination occurs through unbounded recursion. Given a self-recursive rule, we automatically generate one or more devil's rules from it. The construction of the devil's rules is straightforward and involves no guessing. The devil's rules can be simple. For example, they are non-recursive for rules with single recursion. We show that the devil's rules are maximally vicious in the following sense: For any program that contains the self-recursive rule and for any infinite computation through that rule in that program, there is a corresponding infinite computation with the recursive rule and the devil's rules alone. In that case, the malicious rules serve as a finite witness for non-termination. On the other hand, if the devil's rules do not exhibit an infinite computation, the recursive rule is unconditionally terminating. We also identify cases where the static analysis of the devil's rule decides termination or non-termination of the recursive rule.

We present a recursive method to calculate the $\alpha'$-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as $Z$-theory, we pinpoint the equation of motion of $Z$-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order $\alpha'^7$ is made available on the website http://repo.or.cz/BGap.git

We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to build any amplitude in terms of three-gluon amplitudes only.

We construct topological recursion relations (TRR's) at higher genera $g\ge2$ for general 2-dimensional topological field theories coupled to gravity. These TRR's when combined with Virasoro conditions enable one to determine the number of higher genus holomorphic curves in any Fano varieties. In the case of $CP^2$ we reproduce the known results at genus $g=2$.

It is shown that the problem of calculating form factors in ADE affine Toda field theories can be reduced to the nonperturbative recursive calculation of polynomials symmetric in each sort of variables. We determine these recursion equations explicitly for the ADE series and characterize the polynomial solutions by an interplay between the weight space of the underlying Lie algebra and representations of the symmetric group.

This paper examines the completion of an w-ordered sequence of recursive definitions which on the one hand defines an increasing sequence of nested set and on the other redefines successively a numeric variable as the cardinal of the successively defined nested sets. The consequence is a contradiction involving the consistency of w-order and then that of the Axiom of Infinity.

RANGER is an architectural framework for scalable routing and addressing in networks with global enterprise recursion. The term "enterprise network" within this context extends to a wide variety of use cases and deployment scenarios, where an "enterprise" can be as small as a Small Office, Home Office (SOHO) network, as dynamic as a Mobile Ad Hoc Network, as complex as a multi-organizational corporation, or as large as the global Internet itself. Such networks will require an architected solution for the coordination of routing and addressing plans with accommodations for scalability, provider-independence, mobility, multihoming, and security. These considerations are particularly true for existing deployments, but the same principles apply even for clean-slate approaches. The RANGER architecture addresses these requirements and provides a comprehensive framework for IPv6/IPv4 coexistence. This document is not an Internet Standards Track specification; it is published for informational purposes.

"Proof of Brioschi's Recursion Formula for the Expansion of the Even σ-Functions of Two Variables" is an article from American Journal of Mathematics, Volume 21 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369583

This paper aims to develop a rigorous asymptotic analysis of an approximate renormalization group recursion for inverse participation ratios $P_q$ of critical powerlaw random band matrices. The recursion goes back to the work by Mirlin and Evers [37] and earlier works by Levitov [32, 33] and is aimed to describe the ensuing multifractality of the eigenvectors of such matrices. We point out both similarities and dissimilarities of LME recursion to those appearing in the theory of multiplicative cascades and branching random walks and show that the methods developed in those fields can be adapted to the present case. In particular the LME recursion is shown to exhibit a phase transition, which we expect is a freezing transition, where the role of temperature is played by the exponent $q$. However, the LME recursion has features that make its rigorous analysis considerably harder and we point out several open problems for further study

We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect to the latter. New examples of recursion operators obtained using our technique include {\em inter alia} those for the general heavenly equation, which describes a class of anti-self-dual solutions of the vacuum Einstein equations, and a six-dimensional equation resulting from a system of Ferapontov and Khusnutdinova.

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $\sim\frac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.

more polymetric tracks

We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling dependence of the \hat{G}^{2k} \lambda^{16} interaction in type IIB string theory. Using supersymmetry, we show that each of these interactions satisfies a Poisson equation on the moduli space with sources determined by lower momentum interactions. We argue that these protected couplings are only renormalized by a finite number of string loops together with non-perturbative terms. Finally, we explore some consequences of the Poisson equation for low values of k.

Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.

We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size for the even-legged ladder states, it does the opposite for odd-legged ones.

We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjugate to Nijenhuis tensors for a Poisson-Nijenhuis structure defined on the manifold of potentials.

In this article we obtain an explicit formula in terms of the partitions of the positive integer $n$ to express the $n$-th term of a wide class of sequences of numbers defined by recursion. Our proof is based only on arithmetics. We compare our result with similar formulas obtained with different approaches already in the XIX century. Examples are given for Bernoulli, Euler and Fibonacci numbers.

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan's classification and having additional reductions.

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and NNMHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.

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tracks done with polymeters and calling patterns within patterns to create the illusion of more detail than there really is. Sorry if the tracks are a little overlong

Tytuł nagłówkowy. ; Bibliografia na stronach 141-142. ; Streszczenie w języku polskim, rosyjskim. ; artykul w: Annales Universitatis Mariae Curie-Skłodowska. Sectio AAA, Physica Vol. 40/41, 11 (1985/1986), strony 129-142 ; tytul rownolegly: Rekurencyjne związki między współczynnikami genealogicznymi w schemacie seniority ; tytul rownolegly: Rekurrentnye sootnošeniâ meždu genealogičeskimi koèfficientamiv modeli sinʹoriti

Started in 2020, and is still going as of 4/1/2023!

We present on the use of on-shell recursion relations. These can be used not only for calculating tree amplitudes, including those with masses, but also to compute analytically the missing rational terms of one-loop QCD amplitudes. Combined with the cut-containing pieces calculated using a unitarity approach complete one-loop QCD amplitudes can be derived. This approach is discussed in the context of the adjacent 2-minus all-multiplicity QCD gluon amplitude.

Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and \'Esik. Models of these axioms include both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. We show that the standard result on the satisfaction of all Conway axioms by a unique dagger operation generalizes to the guarded setting. We also introduce the notion of guarded trace operator on a category, and we prove that guarded trace and guarded fixpoint operators are in one-to-one correspondence. Our results are intended as first steps leading, hopefully, towards future description of classifying theories for guarded recursion.

In this paper are discussed some formal properties of quantum devices necessary for implementation of nondeterministic Turing machine.

A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained have the same simple form both for ground and excited states and can be easily applied to any renormalization scheme. As an example, the renormalized expansions for the sextic anharmonic oscillator are considered.

We present several recent developments on ELSV-type formulae and topological recursion concerning Chiodo classes and several kind of Hurwitz numbers. The main results appeared in D. Lewanski, A. Popolitov, S. Shadrin, D. Zvonkine, "Chiodo formulas for the r-th roots and topological recursion", Lett. Math. Phys. (2016).

We present several recent developments on ELSV-type formulae and topological recursion concerning Chiodo classes and several kind of Hurwitz numbers. The main results appeared in D. Lewanski, A. Popolitov, S. Shadrin, D. Zvonkine, "Chiodo formulas for the r-th roots and topological recursion", Lett. Math. Phys. (2016).

“- – — .. .. – .-. .- – .- … …. ..- …. …. .- -. -.-. …. ..-. .. -.. .-. .-.. -.. . -. -.-.-“ audio from : ‘Odyssey of Resonance’ by Welentkaam Amt

App Version: 1.0.4 Minimum iOS Version: 11.0 Bundle ID: com.glitchgames.recursion 64-bit: Yes

Recursion is at the leading edge of applying AI and ML to drug development. The company exemplifies a new wave of \"techbio\" companies, that tightly couple compute and robotics with biology and chemistry. The task of decoding biology requires vast amounts of biological data and innovative strategies to make use of that data. It also

An abstract math art design. Designed to print without supports - flat on on the print bed.

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HORATIO & TOMY DECLERQUE - GINGER EARLY SUPPORT FROM CARL COX&ADAM BEYER

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This book is one of the "Popular Lectures in Mathematics" series, widely used by Soviet school mathematics clubs and circles and on teachers' refresher courses. Is a clear introduction for fifth and sixth-form pupils to the variety of recurring series and progressions and their role in mathematics. Is well illustrated with examples and 73 formulas. 

The Beauty and Joy of Computing

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On this Saturday Sidetrack, Tom and Jenny discuss our new, pretty colored lights, Pooky being scared of a morning storm, boobies, and a friend of Tom's who somehow inadvertently pulled an Inception with his t-shirts. Hey! We’re finally on  Instagram ! The Faceless Villain: Volume Three  is now available for purchase in  print  and  ebook  formats! And now the audio book is available too!  Get it here! Click  here  to sign up for Audible! If you buy my book first, I get a bounty! Some of you may remember my short story collection  The Associated Villainies , which I published way back in 2011. Well, I have recently published a second edition, complete with four extra stories, a new cover design, tweaks and corrections to the stories, and a cooler interior layout. Here are the  print  and  ebook  versions, and the audio book version is now available  here ! Please  support us on Patreon ! Don’t forget to follow the  13 O’Clock Podcast blog , subscribe to our  YouTube channel , like us on  Facebook , and follow us on  Twitter . Also, check out our cool merch at our  Zazzle store ! And check out  Giallo Games ! Go subscribe to us over on our  BitChute channel . THANK YOU TO ALL OUR SUPPORTERS! The show is made possible by: Amanda, Anthony, Antonio, Arif, Ashley, Ben, BlackMarigold, Brandon, Christopher, Ciarra, Cody, Corinthian, creepy crepes, Damian, Dan, Dean, Denise, Dominic, Duncan, Dwayne, Ed, Elizabeth, Eric, Fade, Feeky, Gareth, Ginger, Greg, Gwendoline, Hanna, Hayden, Heather, HoboNasty, Holly, Ilse, Ima Shrew, Jaime, Jake A., Jake S., James, James H., Jamin, Jana & Scott, Janet, Jason, Jeanette, Jen, Jessica, Jesus, Joanie, John H., John M., Jonathan, Joseph, Justin, Justyn, Karin, Katrina, Keith, Kieron, Knothead Studios, Kool Kitty, Lana, Lars, Leander, Liam, Lindsey, Lonna, Macy, Marcus, Mary Ellen, Matt, Matthew, Maximillian, Melanie, Melissa, Michael, Mike, Mother of Beasts, Natalia, Nathalie, Nico, Oddcatt, Oli, Paul, Rebecca, Rebecca L., Richard J., Richard & Sheena, Rik, Rob, Robina, Samantha, Sandra, Scarlett, Sean, Sheena, Sophie, Tabitha, Tammie, Tara, Thomm, Tiffany, Tina, Travon, Trevor, Valtrina, Veronica, Via, Victor, Victoria, Victoria E., Virginia, Weaponsandstuff93, Will S., and Xánada. Channel art and audio & video editing by Jenny Ashford. Music & sound effects courtesy of  freesound.org  users jamespotterboy, corsica-s, enjoypa, capturedlv, luffy, kiddpark, and justkiddink. Video clips courtesy of Videezy & Videvo.

On this Saturday Sidetrack, Tom and Jenny discuss our new, pretty colored lights, Pooky being scared of a morning storm, boobies, and a friend of Tom's who somehow inadvertently pulled an Inception with his t-shirts. Hey! We’re finally on  Instagram ! The Faceless Villain: Volume Three  is now available for purchase in  print  and  ebook  formats! And now the audio book is available too!  Get it here! Click  here  to sign up for Audible! If you buy my book first, I get a bounty! Some of you may remember my short story collection  The Associated Villainies , which I published way back in 2011. Well, I have recently published a second edition, complete with four extra stories, a new cover design, tweaks and corrections to the stories, and a cooler interior layout. Here are the  print  and  ebook  versions, and the audio book version is now available  here ! Please  support us on Patreon ! Don’t forget to follow the  13 O’Clock Podcast blog , subscribe to our  YouTube channel , like us on  Facebook , and follow us on  Twitter . Also, check out our cool merch at our  Zazzle store ! And check out  Giallo Games ! Go subscribe to us over on our  BitChute channel . THANK YOU TO ALL OUR SUPPORTERS! The show is made possible by: Amanda, Anthony, Antonio, Arif, Ashley, Ben, BlackMarigold, Brandon, Christopher, Ciarra, Cody, Corinthian, creepy crepes, Damian, Dan, Dean, Denise, Dominic, Duncan, Dwayne, Ed, Elizabeth, Eric, Fade, Feeky, Gareth, Ginger, Greg, Gwendoline, Hanna, Hayden, Heather, HoboNasty, Holly, Ilse, Ima Shrew, Jaime, Jake A., Jake S., James, James H., Jamin, Jana & Scott, Janet, Jason, Jeanette, Jen, Jessica, Jesus, Joanie, John H., John M., Jonathan, Joseph, Justin, Justyn, Karin, Katrina, Keith, Kieron, Knothead Studios, Kool Kitty, Lana, Lars, Leander, Liam, Lindsey, Lonna, Macy, Marcus, Mary Ellen, Matt, Matthew, Maximillian, Melanie, Melissa, Michael, Mike, Mother of Beasts, Natalia, Nathalie, Nico, Oddcatt, Oli, Paul, Rebecca, Rebecca L., Richard J., Richard & Sheena, Rik, Rob, Robina, Samantha, Sandra, Scarlett, Sean, Sheena, Sophie, Tabitha, Tammie, Tara, Thomm, Tiffany, Tina, Travon, Trevor, Valtrina, Veronica, Via, Victor, Victoria, Victoria E., Virginia, Weaponsandstuff93, Will S., and Xánada. Channel art and audio & video editing by Jenny Ashford. Music & sound effects courtesy of  freesound.org  users jamespotterboy, corsica-s, enjoypa, capturedlv, luffy, kiddpark, and justkiddink. Video clips courtesy of Videezy & Videvo.

For those who play Ingress the global Recursion event is going on now. This is a simple badge bearing the event logo. I painted mine with acrylic paint and attached a pin on the back. Your mileage may vary. I found that printing it 3cm in width was the perfect size.