Spherical classes and the Lambda algebra

Let be Singer's invariant-theoretic model of the dual of the lambda algebra with , where denotes the mod 2 Steenrod algebra. We prove that the inclusion of the Dickson algebra, , into is a chain-level representation of the Lannes-Zarati dual homomorphism

The Lannes-Zarati homomorphisms themselves, , correspond to an associated graded of the Hurewicz map

Based on this result, we discuss some algebraic versions of the classical conjecture on spherical classes, which states that Only Hopf invariant one and Kervaire invariant one classes are detected by the Hurewicz homomorphism. One of these algebraic conjectures predicts that every Dickson element, i.e. element in , of positive degree represents the homology class in for 2$">.

We also show that factors through , where denotes the differential of . Therefore, the problem of determining should be of interest.

     

Second-Order Subexponential Sequences and the Asymptotic Behavior of Their De Pril Transform

Suppose that { f(n), n N ₀ } is a sequence of positive real numbers and suppose that the sequence { a(n), n N ₀ } is given by a(0) = 0, and, for n 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) = _f (n) and is called the De Pril transform of { f(n), n N ₀ } . In this paper, we consider first- and second-order asymptotic behavior of { _{f (n), n N 0} } for a large class of subexponential sequences { f(n), n N ₀ } . We also discuss some applications.     

Compact sets of compact operators in absence of

We characterize the compactness of a subset of compact operators between Banach spaces when the domain space does not have a copy of

     

On a differential-algebraic problem

The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.     

Marcinkiewicz–Zygmund Strong Laws for Infinite Variance Time Series

We study rate of convergence in the strong law of large numbers for finite and infinite variance time series in both contexts of weak and strong dependence.     

Global Behavior of Rational Sequences Involving Piecewise Power Function

In this paper, we are concerned with the global behavior ofthe solutions of the difference equation

Shifted Jacobi multiplier sequences and transplantation between sine and cosine series

It is shown that the multiplier norm of a shifted Jacobi multiplier sequence can be estimated by the (same) multiplier norm of the original sequence uniformly with respect to the shift. Muckenhoupt’s transplantation theorem for Jacobi series is used essentially, for which also a functional analytic understanding is given in terms of the minimality of the Jacobi system in weighted L ^p -spaces.      

On the Space bvp（F） of Sequences of p-bounded Variation of Fuzzy Numbers

Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.     

The use of phase codes in ultrasound imaging: SNR gain and bandwidth requirements

Most of the literature on coded excitation describes the signal-to-noise ratio gain of a coded waveform in terms of the time-bandwidth product. We have shown that in the context of ultrasound imaging, the expression for the SNR gain provided by matched filtering a coded waveform, can be reduced to the total number of chips in the transmit signal. Hence, the SNR gain is independent of both the bandwidth and the duration of a single-chip. This concept is described in detail, clarifying this seeming contradiction. The impact of bandwidth and pulse duration on the SNR, SNR gain and axial resolution is described. Bandwidth requirements and the impact of regulatory peak-power limitations are also addressed.