We construct a collection of families of higher Chow cycles of type $(2,1)$ on a two-dimensional family of Kummer surfaces, and prove that for a very general member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of the higher Chow group. Construction of the cycles uses a finite group action on the family, and the proof of their linear independence uses Picard–Fuchs differential operators.

We prove the Gross–Deligne conjecture on CM periods for motives associated with ${{H}^{2}}$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the ${{K}_{1}}$-regulators in terms of hypergeometric functions $_{3}{{F}_{2}}$, and obtain a new example of non-trivial regulators.

Prediction of gas-production-induced subsidence and seismicity is much more difficult and uncertain than generally recognised in the past. It is now widely accepted that uncertainties in predicted subsidence and seismicity are large prior to and during the initial stages of production. At later stages, predictions remain highly uncertain for periods more than three to five years into the future. This requires a different regulatory framework to ensure that associated risks remain within accepted boundaries. Previously, single-scenario operator predictions were checked against field measurements. When subsidence or seismicity started to deviate beyond claimed uncertainties, the operator was asked to provide prediction updates. The practice was long considered acceptable, as structural damage to buildings and infrastructure or personal risk to people was not expected. This all changed following the 2012 Huizinge seismic event, necessitating better identification, assessment and ranking of risks, the use of scenarios, probabilistic forecasting and a much intensified field monitoring and control loop. It requires that the regulator becomes actively involved in assuring the integrated control loop of risk identification, predictions, monitoring, updating, mitigation measures and the closing of knowledge gaps, to ensure that subsidence (rate) and induced seismicity remain within acceptable limits. And it requires that this increased involvement of the regulator is supported in the mining law and by appropriate conditions in the Production Plan assent.

We explicitly find regulators of an infinite family $\{{{L}_{m}}\}$ of the simplest quartic function fields with a parameter $m$ in a polynomial ring ${{\mathbb{F}}_{q}}\left( t \right)$, where ${{\mathbb{F}}_{q}}$ is the finite field of order $q$ with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields having the same conductors. We obtain a lower bound on the class numbers of the family $\{{{L}_{m}}\}$ and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain $\{{{L}_{m}}\}$ as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field ${{\mathbb{F}}_{q}}\left( t \right)$ in $\{{{L}_{m}}\}$.

Let $n$ be a positive even integer, and let $F$ be a totally real number field and $L$ be an abelian Galois extension which is totally real or $\text{CM}$. Fix a finite set $S$ of primes of $F$ containing the infinite primes and all those which ramify in $L$, and let ${{S}_{L}}$ denote the primes of $L$ lying above those in $S$. Then $\mathcal{O}_{L}^{S}$ denotes the ring of ${{S}_{L}}$-integers of $L$. Suppose that $\psi$ is a quadratic character of the Galois group of $L$ over $F$. Under the assumption of the motivic Lichtenbaum conjecture, we obtain a non-trivial annihilator of the motivic cohomology group $H_{\mathcal{M}}^{2}\left( \mathcal{O}_{L}^{S},\mathbb{Z}\left( n \right) \right)$ from the lead term of the Taylor series for the S-modified Artin $L$-function $L_{L/F}^{S}\left( s,\psi \right)$ at $s=1-n$.

This paper introduces a VDD generator for the ultrahigh frequency (UHF) passive Radio-frequency identification (RFID) tag, consisting of an RF-limiter, an NMOS rectifier, a DC-limiter, and a regulator. The proposed NMOS rectifier utilizes diode-connected native NMOS transistors with ultralow-threshold voltage instead of Schottky diodes. The theoretical equations for predicting the performance of the VDD generator are provided and verified by both simulation results in 90 nm CMOS process. The proposed VDD generator generates a 1.19-V stable output voltage with low-power dissipation and a 26.96% larger power conversion efficiency under conditions of 50 Ω antenna, 900 MHz, −23 dBm input power and 1 M DC output load. The chip area of the proposed VDD generator is only 105 × 85 μm. The simulation results indicated that the presented novel VDD generator is capable to provide efficient, stable, and input-independent power supply for Passive UHF RFID tag

Let U/ℂ be a smooth quasi-projective variety of dimension d, CHr (U,m) Bloch's higher Chow group, and

clr,m: CHr (U,m) ⊗ ℚ → homMHS (ℚ(0), H2r−m (U, ℚ(r)))

the cycle class map. Beilinson once conjectured clr,m to be surjective [Be]; however, Jannsen was the first to find a counterexample in the case m = 1 [Ja1]. In this paper we study the image of clr,m in more detail (as well as at the “generic point” of U) in terms of kernels of Abel-Jacobi mappings. When r = m, we deduce from the Bloch-Kato conjecture (now a theorem) various results, in particular that the cokernel of clm,m at the generic point is the same for integral or rational coefficients.

This paper is concerned with the methods of mathematical modeling of thesocio-economicdevelopment of regions. The objective of this study is to analyze and assess thesocio-economicpotential of the territory having regard to its individual socio-economic andeconomic-geographicalcharacteristics. The territory's individual characteristics, in turn, aretreated as invariantconditions of its development. The study territory includes regions and federaldistricts of theRussian Federation.
An assessment of the regions' development potential is made from the perspectiveof analyzingtheir current socio-economic situation for the time interval 1999-2002 takenfrom official statisticalhandbooks. To accomplish this, a special-purpose mathematical model is developedin the formof a hierarchical fractal indicative function relating the generalized indicatorcharacterizing theregions' development potential, or the “indicated” (that which is indicatedversus indicator), to theparticular socio-economic characteristics of the territory, or the developmentindicators of the localeconomy, via the model coefficients which is termed regulators.
As a result, the economic-mathematical model is generated in the form of anindicative functioncharacterizing the current socio-economic situation of the regions and federaldistricts of Russiaon different levels of economic organization (from local and regional tonational). It reflects appropriatelyand dramatically the specific character of the region's socio-economic potentialby theexample of the connection of investments with the volumes of production. Themodel permitsthe position of the regions and districts to be identified in the system ofinter-regional and nationalsocio-economic links and economic-geographical conditions of development. Theresultsderived from modeling the socio-economic development potential of Russia'sregions have beenused to construct the control surface of the country's economy characterizingthe changes in the development potential of the federal districts toward itsdecrease.

Starting from the candidate Bloch-Beilinson filtration on constructed in [L2], we develop and describe geometrically a series of Hodgetheoretic invariants Ψi defined on the graded pieces. Explicit formulas (in terms of currents and membrane integrals) are given for certain quotients of the Ψi, with applications to 0-cycles on products of curves.

We construct families of hyperelliptic curves over ${\mathbb Q}$ of arbitrary genus g with (at least) g integral elements in K2. We also verify the Beilinson conjectures about K2 numerically for several curves with g = 2, 3, 4 and 5. The first few sections of the paper also provide an elementary introduction to the Beilinson conjectures for K2 of curves.

We construct a map between Bloch's higher Chow groups and Deligne homology for smooth, complex quasiprojective varieties on the level of complexes. For complex projective varieties this results in a formula which generalizes at the same time the classical Griffiths Abel–Jacobi map and the Borel/Beilinson/Goncharov regulator type maps.

Let X/C be a projective algebraic manifold, and further let CHk(X)Q be the Chow group of codimension k algebraic cycles on X, modulo rational equivalence. By considering Q-spreads of cycles on X and the corresponding cycle map into absolute Hodge cohomology, we construct a filtration {F[ell ]}[ell ] [ges ] 0 on CHk(X)Q of ‘Bloch-Beilinson’ type. In the event that a certain conjecture of Jannsen holds (related to the Bloch-Beilinson conjecture on the injectivity, modulo torsion, of the Abel–Jacobi map for smooth proper varieties over Q), this filtration truncates. In particular, his conjecture implies that Fk+1 = 0.

In this paper we study the group K2n(n+1)(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson–Soulé conjecture on weights. In particular, we compute the Beilinson regulator on a subgroup of K2n(n+1)(F), using the complexes constructed in Compositio Math. 96 (1995), pp. 197–247. We study the boundary map in the localization sequence for n=2 and n=3. We combine our results with results of Goncharov in order to obtain a complete description of the image of the regulator map on K4(3)(C) and K6(4)(C) (which have the same images as K4(C)$⊗ _{\Bbb Z}\, {\Bbb Q}$, and K6(C)$⊗ _{\Bbb Z}\, {\Bbb Q}$, respectively), independent of any conjectures.

In an earlier paper we developed an algorithm for computing all integral points on elliptic curves over the rationals Q. Here we illustrate our method by applying it to Mordell‘s Equation y$^2$=x$^3+$k for 0 ≠ k ∈ Z and draw some conclusions from our numerical findings. In fact we solve Mordell‘s Equation in Z for all integers k within the range 0 < | k | [les ] 10 000 and partially extend the computations to 0 < | k | [les ] 100 000. For these values of k, the constant in Hall‘s conjecture turns out to be C=5. Some other interesting observations are made concerning large integer points, large generators of the Mordell–Weil group and large Tate–Shafarevič groups. Three graphs illustrate the distribution of integer points in dependence on the parameter k. One interesting feature is the occurrence of lines in the graphs.