A renormalization group proof of perturbative renormalizability

This paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean ₄ ⁴ theory. Its aim is partly pedagogical: by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages. The present version is based on the renormalized tree expansion adapted to the continuous renormalization group: all detailed results are proved by induction on the size of the tree. The continuous RG version presented here has one big advantage over the discrete RG version discussed elsewhere. In the continuous version, a tree has a more restrictive structure: there is a one-to-one correspondence between forks of the tree and lines of Feynman graphs. This extra structure eliminates the need to introduce Feynman graphs in the first place. It also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates.Research supported by the Natural Sciences and Engineering Research Council     

Discrimination of frequency transitions by human infants

Difference limens (DLs) for linear frequency transitions using a 1.0-kHz pulsed-tone standard were obtained from 6- to 9-month-old human infants in a series of three experiments. A repeating standard "yes-no" operant headturning technique and an adaptive staircase (tracking) procedure were used to obtain difference limens from a total of 71 infants. The DLs for 300-ms upward and downward linear frequency sweeps were approximately 3%-4% when the repeating standard was an unmodulated 1.0-kHz pulsed tone of 300-ms duration. These DLs for frequency sweeps were not significantly different from DLs for frequency increments and decrements using 330-ms pulsed tones [J. M. Sinnott and R. N. Aslin, J. Acoust. Soc. Am. 78, 1986-1992 (1985)]. The DLs for frequency sweeps of 50 ms appended to the beginning or the end of a 250-ms unmodulated 1.0-kHz tone were approximately 6%-7%. This greater DL for brief frequency sweeps was confirmed by varying the duration but not the extent of the sweep. Finally, DLs were greater than 50% when the repeating standard was a 50-ms rising or falling frequency sweep appended to the beginning of a 250-ms unmodulated 1.0-kHz tone. These results suggest that rapid frequency transitions are much more difficult to discriminate from frequency transitions of the same category (rising or falling) than from either a frequency transition of the opposite category (falling or rising) or an unmodulated tone.(ABSTRACT TRUNCATED AT 250 WORDS)     

Oscillatory and Asymptotic Behavior of Damped Functional Differential Equations

New theorems on the oscillatory and asymptotic behavior of solutions of the damped differential equations with deviating arguments of the form are established.     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

On consistency of bounding operations in deterministic global optimization

This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence _q in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.     

Metastable patterns in solutions of ut = ϵ2uxx − f(u)

We consider the equation in question on the interval 0 ≦ x ≦ 1 having Neumann boundary conditions, with f(u) = F(u), where F is a double well energy density with equal minima at u = ±1. The only stable states of the system are patternless constant solutions. But given two-phase initial data, a pattern of interfacial layers typically forms far out of equilibrium. The ensuing nonlinear relaxation process is extremely slow: patterns persist for exponentially long times proportional to exp{A_±l/?, where A = F(±1) and l is the minimum distance between layers. Physically, a tiny potential jump across a layer drives its motion. We prove the existence and persistence of these metastable patterns, and characterise accurately the equations governing their motion. The point of view is reminiscent of center manifold theory: a manifold parametrising slowly evolving states is introduced, a neighbourhood is shown to be normally attracting, and the parallel flow is characterised to high relative accuracy. Proofs involve a detailed study of the Dirichlet problem, spectral gap analysis, and energy estimates.     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -