Study of an auroral zone rocket experiment Final report

Measurement of flux and energy spectra of protons, energetic particles, hydrogen atoms, and electrons in auroral zone by Nike-Tomahawk sounding rocke

External Validity and Evaluation Research: A Codification of Problems

This paper delimits and explicates threats to external validity particularly problematic in evaluation research. Five categories of factors are discussed: selection effects, measurement effects, confounded treatment effects, situational effects, and effects due to differential mortality. The paper focuses on pointing up specific ways in which each of the factors threaten generalizability and possible solutions to the methodological problems presented

Transformation laws of the components of classical and quantum fields and Heisenberg relations

The paper recalls and point to the origin of the transformation laws of the components of classical and quantum fields. They are considered from the "standard" and fibre bundle point of view. The results are applied to the derivation of the Heisenberg relations in quite general setting, in particular, in the fibre bundle approach. All conclusions are illustrated in a case of transformations induced by the Poincar\'e group.Comment: 22 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. For other papers on the same topic, view http://theo.inrne.bas.bg/~bozho/ . arXiv admin note: significant text overlap with arXiv:0809.017

The dopaminergic midbrain participates in human episodic memory formation: Evidence from genetic imaging

Recent data from animal studies raise the possibility that dopaminergic neuromodulation promotes the encoding of novel stimuli. We investigated a possible role for the dopaminergic midbrain in human episodic memory by measuring how polymorphisms in dopamine clearance pathways affect encoding-related brain activity (functional magnetic resonance imaging) in an episodic memory task. In 51 young, healthy adults, successful episodic encoding was associated with activation of the substantia nigra. This midbrain activation was modulated by a functional variable number of tandem repeat (VNTR) polymorphism in the dopamine transporter (DAT1) gene. Despite no differences in memory performance between genotype groups, carriers of the (low expressing) 9-repeat allele of the DAT1 VNTR showed relatively higher midbrain activation when compared with subjects homozygous for the 10-repeat allele, who express DAT1 at higher levels. The catechol-O-methyl transferase (COMT) Val108/158Met polymorphism, which is known to modulate enzyme activity, affected encoding-related activity in the right prefrontal cortex (PFC) and in occipital brain regions but not in the midbrain. Moreover, subjects homozygous for the (low activity) Met allele showed stronger functional coupling between the PFC and the hippocampus during encoding. Our finding that genetic variations in the dopamine clearance pathways affect encoding-related activation patterns in midbrain and PFC provides strong support for a role of dopaminergic neuromodulation in human episodic memory formation. It also supports the hypothesis of anatomically and functionally distinct roles for DAT1 and COMT in dopamine metabolism, with DAT1 modulating rapid, phasic midbrain activity and COMT being particularly involved in prefrontal dopamine clearance

A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups

We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras. Our main result can be considered as a quantum analog of a result by Y. Bazlov

Detecting brute-force attacks on cryptocurrency wallets

Blockchain is a distributed ledger, which is protected against malicious modifications by means of cryptographic tools, e.g. digital signatures and hash functions. One of the most prominent applications of blockchains is cryptocurrencies, such as Bitcoin. In this work, we consider a particular attack on wallets for collecting assets in a cryptocurrency network based on brute-force search attacks. Using Bitcoin as an example, we demonstrate that if the attack is implemented successfully, a legitimate user is able to prove that fact of this attack with a high probability. We also consider two options for modification of existing cryptocurrency protocols for dealing with this type of attacks. First, we discuss a modification that requires introducing changes in the Bitcoin protocol and allows diminishing the motivation to attack wallets. Second, an alternative option is the construction of special smart-contracts, which reward the users for providing evidence of the brute-force attack. The execution of this smart-contract can work as an automatic alarm that the employed cryptographic mechanisms, and (particularly) hash functions, have an evident vulnerability.Comment: 10 pages, 2 figures; published versio

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Representations of the Generalized Lie Algebra sl(2)_q

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra \ssll (2)_q introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic and $q$ at roots of unity. Some of the representations have no classical analog even for generic $q$. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra $U_q(sl(2))$, while in those that do there are different matrix elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de

On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory

Given a particular solution of a one-dimensional stationary Schroedinger equation (SE) this equation of second order can be reduced to a first order linear differential equation. This is done with the aid of an auxiliary Riccati equation. We show that a similar fact is true in a multidimensional situation also. We consider the case of two or three independent variables. One particular solution of (SE) allows us to reduce this second order equation to a linear first order quaternionic differential equation. As in one-dimensional case this is done with the aid of an auxiliary Riccati equation. The resulting first order quaternionic equation is equivalent to the static Maxwell system. In the case of two independent variables it is the Vekua equation from theory of generalized analytic functions. We show that even in this case it is necessary to consider not complex valued functions only, solutions of the Vekua equation but complete quaternionic functions. Then the first order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of (SE) and the other can be considered as an auxiliary equation of a simpler structure. For the auxiliary equation we always have the corresponding Bers generating pair, the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of (SE). We obtain an analogue of the Cauchy integral theorem for solutions of (SE). For an ample class of potentials (which includes for instance all radial potentials), this new approach gives us a simple procedure allowing to obtain an infinite sequence of solutions of (SE) from one known particular solution