Using the formalism of nonlinear realizations we construct the component on-shell action of the N =3D 4, d =3D 3 Born-Infeld theory, which is the action of N =3D 2, d =3D 3 vector supermultiplet, fixed by invariance with respect to the additional spontaneously broken N =3D 2, d =3D 3 supersymmetry. Our construction shows that dealing with the systems with partial breaking of supersymmetry with vector fields in the multiplet, it is preferrable to use their formulation in terms of fermionic superfields only.
In this paper, we first prove that, for a non-zero function faD(a"e (n) ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' (H) (a"e (n) ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' (H) (a"e (n) ) is the biggest subspace of D'(a"e (n) ) on which the extended multi-Hilbert transform is a homeomorphism.
Nikola Adžaga
Andrej Dujella
Dijana Kreso
Petra Tadić
Abstract For a nonzero integer n , a set of distinct nonzero integers { a 1 , a 2 , … , am } such that a ia j + n is a perfect square for all 1 ≤ i < j ≤ m , is called a Diophantine m -tuple with the property D ( n ) or simply D ( n ) -set. D ( 1 ) -sets are known simply as Diophantine m -tuples. Such sets were first studied by Diophantus of Alexandria, and since then by many authors. It is natural to ask if there exists a Diophantine m -tuple (i.e. D ( 1 ) -set) which is also a D ( n ) -set for some n ≠ 1 . This question was raised by Kihel and Kihel in 2001. They conjectured that there are no Diophantine triples which are also D ( n ) -sets for some n ≠ 1 . However, the conjecture does not hold, since, for example, { 8 , 21 , 55 } is a D ( 1 ) and D ( 4321 ) -triple, while { 1 , 8 , 120 } is a D ( 1 ) and D ( 721 ) -triple. We present several infinite families of Diophantine triples { a , b , c } which are also D ( n ) -sets for two distinct n 's with n ≠ 1 , as well as some Diophantine triples which are also D ( n ) -sets for three distinct n 's with n ≠ 1 . We further consider some related questions.
Let R be a ring, n, d be fixed non-negative integers, T-n,T-d the class of (n, d)-injective left R-modules, and F-n,F-d the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m >=3D 2, then gl-right-T-n,T-d-dim(R)M <=3D m if and only if gl-left-T-n,T-d-dim(R)M <=3D m - 2, if and only if Ext(m)+k(M, N) =3D 0 for all left R-modules M, N and all k >=3D -1, if and only if Ext(m-1)(M, N) =3D 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then -circle times- is right balanced on M-R x (R) M by F-n,F-d X T-n,T-d, and investigate the global right T-n,T-d-dimension of M-R and the global right Tmd-dimension of M-R by right derived functors of (8). Some known results are obtained as corollaries.
Konobeevsky, E.
Kasparov, A.
Mordovskoy, M.
Zuyev, S.
Lebedev, V.
Spassky, A.
A kinematically complete measurement of the four -body breakup reaction d+H-2 ->(2)p(S)+(2)n(S)-> p +p +n +n has been performed at 15 MeV deuteron beam of the SINP MSU. The two protons and neutron were detected at angles close to those of emission of (2)p(S) and (2)n(S) systems. The energy of singlet dineutron state was determined by comparing experimental TOF spectrum of breakup neutrons with simulated spectra depending on this energy. A low value E-nn =3D 0.076 +/- 0.006 keV obtained by fitting procedure apparently indicates an effective enhancement of nn -interaction in the intermediate state of studied reaction.
Chappell, Isaac
Gates, S. James, Jr.
Linch, William D., III
Parker, James
Randall, Stephen
Ridgway, Alexander
Stiffler, Kory
The off-shell representation theory of 4D, N = 1 supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras as part of a larger effort we call supersymmetry 'genomics.' Recent evidence has emerged pointing to the existence of three such fundamental adinkras associated with distinct equivalence classes of a Coxeter group. A partial description of these adinkras is given in terms of two types, termed cis-and trans-adinkras (the latter being a degenerate doublet) in analogy to cis/trans isomers in chemistry. Through a new and simple procedure that uses adinkras, we find the irreducible off-shell adinkra representations of 4D, N = 1 supergravity, in the old-minimal, non-minimal, and conformal formulations. This procedure uncovers what appears to be a selection rule useful to reverse engineer adinkras to higher dimensions. We categorize the supergravity representations in terms of the number of cis-(n(c)) and trans-(n(t)) adinkras in the representation and synthesize our new results with our previous supersymmetry genomics results into a group theoretic framework.
Horak, Martin
Holubova, Kristina
Nepovimova, Eugenie
Krusek, Jan
Kaniakova, Martina
Korabecny, Jan
Vyklicky, Ladislav
Kuca, Kamil
Stuchlik, Ales
Ricny, Jan
Vales, Karel
Soukup, Ondrej
Effect of tacrine on glutamatergic neurons is both direct and indirect. Indirect via M1 receptor leading to inhibition of Ca2 +-activated K channels. Such inhibition prevents membrane repolarization leading to long term potentiation. Tacrine possesses dual mechanism of action.
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in the D=3D8 N=3D1 supersymmetric Yang-Mills theory in the planar limit for ladder-type diagrams. We obtain recurrence relations that allow obtaining the leading and subleading divergences in all loops purely algebraically starting from the one-loop diagrams (for the leading poles) and the two-loop diagrams (for the subleading poles). We sum the leading and subleading divergences over all loops using differential equations that are generalizations of the renormalization group equations to nonrenormalizable theories. We discuss the properties of the obtained solutions and the dependence of the constructed counterterms on the scheme.