We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the ...DeGeorge–Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini–Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the possible limits. We show that BS-convergence of locally symmetric spaces Γ\G/K implies convergence, in an appropriate sense, of the normalized relative Plancherel measures associated to L 2 (Γ\G). This then yields convergence of normalized multiplicities of unitary representations, Betti numbers and other spectral in-variants. On the other hand, when the corresponding Lie group G is simple and of real rank at least two, we prove that there is only one possible BS-limit, i.e. when the volume tends to infinity, locally symmetric spaces always BS-converge to their universal cover G/K. This leads to various general uniform results. When restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of BS-convergence which in turn implies upper estimates on the rate of convergence of normalized Betti numbers in the spirit of Sarnak–Xue. An important role in our approach is played by the notion of Invariant Random Subgroups. For higher rank simple Lie groups G, we exploit rigidity theory, and in particular the Nevo–Stück–Zimmer theorem and Kazhdan's property (T), to obtain a complete understanding of the space of IRSs of G.
We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is ...deduced from the main result about finite groups: let w be a 'locally finite' group word and $d\in {\Bbb N}$ . Then there exists f = f(w, d) such that in every d-generator finite group G, every element of the verbal subgroup w(G) is equal to a product of f w-values. An analogous theorem is proved for commutators; this implies that in every finitely generated profinite group, each term of the lower central series is closed. The proofs rely on some properties of the finite simple groups, to be established in Part II.
We prove two results. (1) There is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D 'twisted ...commutators' defined by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M = M(q) such that: if S is a finite quasisimple group with $|S/Z(S)|>C,\beta _{j}(j=1,...,M)$ are any automorphisms of S, and $q_{j}(j=1,...,M)$ are any divisors of q, then there exist inner automorphisms $\alpha _{j}$ of S such that $S=\Pi _{1}^{M}S,(\alpha _{j}\beta _{j})^{q_{j}}$ . These results, which rely on the classification of finite simple groups, are needed to complete the proofs of the main theorems of Part I.
We propose and explore financial instruments supporting programs for reducing emissions from deforestation and forest degradation (FI-REDD). Within a microeconomic framework we model interactions ...between an electricity producer (EP), electricity consumer (EC), and forest owner (FO). To keep their profit at a maximum, the EP responds to increasing
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prices by adjusting electricity quantities generated by different technologies and charging a higher electricity price to the EC. The EP can prepare for future high (uncertain)
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prices by employing FI-REDD: they can purchase an amount of offsets under an unknown future
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price and later, when the
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price is discovered, decide how many of these offsets to use for actually offsetting emissions and sell the rest on the market, sharing the revenue with the FO. FI-REDD allows for optional consumption of emission offsets by the EP (any amount up to the initially contracted volume is allowed), and includes a benefit-sharing mechanism between the EP and FO as it regards unused offsets. The modeling results indicate that FI-REDD might help avoid bankruptcy of
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-intensive producers at high levels of
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prices and therefore serve as a stabilizing mechanism during the transition of energy systems to greener technologies. The analytical results demonstrate the limits for potential market size explained by existing uncertainties. We illustrated that when suppliers and consumers of REDD offsets have asymmetric information on future
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prices, benefit-sharing increases the contracted REDD offsets quantity.
Active RC LPFs with Single-Element Pole Frequency Tuning Denisenko, Darya Yurievna; Prokopenko, Nikolay Nikolaevich; Butyrlagin, Nikolav Vladimirovich
2020 XI National Conference with International Participation (ELECTRONICA),
2020-July-23
Conference Proceeding
New low-pass filter (LPF) architectures based on differential difference operational amplifiers (DDOA) are studied in this paper. The feature of the proposed LPF is that when tuning the cut-off ...frequency, the LPF gain remains unchanged at zero frequency. As a tuning element, it is possible to use digital potentiometers. The basic equations for two LPF modifications are presented, which provide parametric synthesis of circuits. The results of computer simulation of tunable responses were given in Micro-cap CAD.
The authors are involved in a project devoted to development of new methods for setting up of relay protection (RP) of modern electric power systems (EPS) using detailed mathematical models, which ...take into account the specific features of RP and processes in transducers. Results presented in the paper show that numerical methods of integration are badly applicable for solving even simple mathematical model of RP. Such conclusion was made due to obvious distortion of the simulated signals. An alternative to numerical modeling is the so-called hybrid approach, on the basis of which a simulator of EPS - Hybrid Real Time Simulator (HRTSim) was created. This approach was applied for development of software and hardware element compatible with the HRTSim. Test of the element was performed and there is no distortion appears in the output simulated signal.
Game theory Petrosjan, Leon A; Petrosjan, Leon A; Zenkevich, Nikolay A
1996., 1996, 19960209, Letnik:
3
eBook
Game theory is a branch of modern applied mathematics that aims to analyze various problems of conflict between parties that have opposed, similar or simply different interests.
A systematic investigation of the electric parameters of the CuBr laser plasma during the excitation pulse in their correlation to the laser output characteristics is presented. Based on the electric ...parameters, the temporal course is calculated of the electron density during the discharge. The authors offer a simple mechanism which generally explains how the hydrogen occurred in the copper vapor laser. The mechanism consists of shielding copper ionization by the process of electron detachment from negative hydrogen ions.< >
The O-specific polysaccharide was obtained by mild degradation of the Salmonella arizonae O61 lipopolysaccharide with acid. It contained 2-acetamido-2-deoxy-D-glucose, ...2-acetamidino-2,6-dideoxy-L-galactose (FucAm), and 7-acetamido-3,5,7,9-tetradeoxy-5-(R)-3-hydroxybutyramido-D- glycero-L-galacto-nonulosonic acid (Sug). On the basis of partial acid hydrolysis with 0.1 M HCl, solvolysis with anhydrous HF in methanol, and 1H- and 13C-NMR analysis (including 1H/13C inversely correlated spectroscopy for localisation of N-acyl substituents), it was concluded that the O-specific polysaccharide had the following structure. ---3)-alpha-L-FucAm-(1---3)-alpha-D-GlcNAc-(1---8)-beta-Sug+ ++-(2--- The O-antigen of S. arizonae O61 is structurally related to that of Pseudomonas aeruginosa O12, thus explaining the known serological cross-reactivity between these micro-organisms.
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