Miracle-dz/UniFAR-FTUs huggingface dataset:
On the k-regularity of the k-adic valuation of Lucas sequences

For integers $k \geq 2$ and $n \neq 0$, let $v_k(n)$ denotes the greatest nonnegative integer $e$ such that $k^e$ divides $n$. Moreover, let $u_n$ be a nondegenerate Lucas sequence satisfying $u_0 = 0$, $u_1 = 1$, and $u_{n + 2} = a u_{n + 1} + b u_n$, for some integers $a$ and $b$. Shu and Yao showed that for any prime number $p$ the sequence $v_p(u_{n + 1})$ is $p$-regular, while Medina and Rowland found the rank of $v_p(F_{n + 1})$, where $F_n$ is the $n$-th Fibonacci number. We prove that if $k$ and $b$ are relatively prime then $v_k(u_{n + 1})$ is a $k$-regular sequence, and for $k$ a prime number we also determine its rank. Furthermore, as an intermediate result, we give explicit formulas for $v_k(u_n)$, generalizing a previous theorem of Sanna concerning $p$-adic valuations of Lucas sequences.
Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material

The spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material (LHM) is investigated. We first consider the case of the atom being in front of a LHM layer mounted on a mirror, where it has been claimed that the atomic decay would be inhibited completely. Here we introduce dispersion and dissipation in the LHM, and find that there are two factors that weaken the inhibition of spontaneous decay. One is atomic nonradiative decay at shorter distances and the other is the instantaneous radiative decay process for larger distances. Then we discuss the decay process of an atom embedded in a one-dimensional photonic crystal composed of alternate LHM and ordinary material [right-handed material (RHM)] layers (LHM-RHM PC). Because of two special characteristics of the LHM, phase compensation and the fact that a frequency with negative index is usual near the material resonance frequency, both the radiative and nonradiative decay processes in the LHM-RHM PC are much different from those in a RHM PC. Under appropriate condition, the population evolution of atoms in a LHM-RHM PC displays oscillatory behavior.
Dyakonov–Tamm waves-based optical sensing using sculptured nematic thin film

Abstract. Dyakonov–Tamm (DT) waves are highly sensitive to the constitutive properties of the partnering materials near the interface. DT waves are excited at the interface of two dielectric materials of which at least one is anisotropic and periodically nonhomogeneous normal to their interface. Sculptured nematic thin film (SNTF) is a good candidate for the periodically nonhomogeneous dielectric partner for optical sensing of a fluid due to its porosity. The nanoscale parameters of an uninfiltrated SNTF obtained from the inverse Bruggeman homogenization formalism were used in the forward Bruggeman homogenization formalism to determine the constitutive parameters for the infiltrated SNTF. The sensitivity of DT waves to the refractive index was analyzed for two possible sensing modalities and it was found that the sensitivity was comparable to that of the chiral sculptured thin films (STFs) made of the same material as of the SNTF. This implies that the sensing with DT waves is robust, is independent of the morphology of the partnering nonhomogeneous dielectric material and could make the sensing easier since SNTFs are easier to fabricate than the chiral STFs.
Global well-posedness for the Euler alignment system with mildly singular interactions

We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved in [, –]. Here, we consider a class of less singular interaction kernels and establish the global regularity of solutions as long as the interaction kernels are not integrable. The proof relies on modulus of continuity estimates for a class of parabolic integro-differential equations with a drift and mildly singular kernels.
Constituents and their expectation : towards a critical-pragmatic theory of information systems project management

ion and generalization Relating the details revealed by the data interpretation to theoretical, general concepts that describe the nature of human understanding and social action. The use of action research provided the opportunity to develop theory based in practice, but applicable to other situations, as only the methodology-for-use derived from the theory was tailored to the research setting Dialogical reasoning Sensitivity to possible contradictions between initial positions and the need for revision The action research resulted in the development of a theoretical model, and this was subsequently augmented as a result of the meta-study; the overall goal was theory development, not confirming existing theory Multiple interpretations Sensitivity to the possibility of different interpretations of the same event The research setting enabled the different viewpoints of the project team to be openly discussed Suspicion Sensitivity to the possibility to bias and distortion in the narratives provided by the participants The organizational setting and the use of some of the data for operational purposes required that the integrity of the data be assessed continually Table 3.2: Applying the Seven Principles of Qualitative IS Research Source: Based on Klein and Myers (1999, p72)
Balanced Phase Field model for Active Surfaces

In this paper we present a balanced phase field model for active surfaces. This work is devoted to the generalization of the Balanced Phase Field Model for Active Contours devised to eliminate the often undesirable curvature-dependent shrinking of the zero level set while maintaining the smooth interface necessary to calculate the fundamental geometric quantities of the represented contour. As its antecedent work, the proposed model extends the Ginzburg-Landau phase field energy with a higher order smoothness term. The relative weights are determined with the analysis of the level set motion in a curvilinear system adapted to the zero level set. The proposed model exhibits strong shape maintaining capability without significant interference with the active (e.g. a segmentation) model.
The Low Temperature Magnetoconductance of Delta-Doped Silicon

Title of dissertation: THE LOW TEMPERATURE MAGNETOCONDUCTANCE OF DELTA-DOPED SILICON Dan Francis Sullivan, Doctor of Philosophy, 2005 Dissertation directed by: Dr. Bruce E. Kane Department of Physics The low temperature electronic transport properties of delta-doped silicon are established here, in an effort to determine the technological limitations facing the construction of semiconductor wafers with monolayer doping profiles. Both phosphorous (Si:P) and boron (Si:B) delta-doped silicon wafers prepared by molecular beam epitaxy have been investigated. Devices fabricated from samples of these wafers were cooled to approximately 130 mK in a dilution refrigerator, where four wire resistance measurements were performed in the presence of magnetic fields both perpendicular and parallel to the plane of the devices. The data obtained was interpreted using the theory of weak localization. For Si:P samples, the effective thickness of the delta-doped region can be inferred by comparing the magnetoconductance signal in parallel magnetic fields to that of perpendicular fields. Using this technique on several different samples which were annealed at 850 ◦C, an estimate of the diffusivity of phosphorus in silicon at this temperature is established. In addition, it is shown that the primary mechanism for the loss of quantum mechanical phase coherence in these samples at low temperatures is the electron-electron interaction, and provide evidence for lattice defects enhancing this dephasing. For Si:B samples, the spin-orbit interaction is shown to dominate the dephasing, and the temperature dependence of this interaction is found to be substantially different from that observed in Si:P devices. Based on these results, I conclude that specific epitaxial growth techniques must be followed if monolayer doping profiles are ever to be achieved in silicon. In addition, because this weak localization technique for measuring the thickness of delta-doped regions is highly sensitive and non-destructive, it may ultimately prove to be the most effective method yet established for probing ultra-thin doping profiles. Finally, several theoretical desiderata are established, which would enable a more accurate interpretation of experimental data. THE LOW TEMPERATURE MAGNETOCONDUCTANCE OF DELTA-DOPED SILICON
Counterexamples for percolation on unimodular random graphs

We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with $p_c=p_u$ for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with $p_c<1$ but with an infinite cluster at criticality. These examples show that two well-known conjectures of Benjamini and Schramm are false when generalised from transitive graphs to unimodular random rooted graphs.
Identification of Markers for Diagnosis and Treatment of Diabetic Kidney Disease Based on the Ferroptosis and Immune

Background In advanced diabetic kidney disease (DKD), iron metabolism and immune dysregulation are abnormal, but the correlation is not clear. Therefore, we aim to explore the potential mechanism of ferroptosis-related genes in DKD and their relationship with immune inflammatory response and to identify new diagnostic biomarkers to help treat and diagnose DKD. Methods Download data from gene expression omnibus (GEO) database and FerrDb database, and construct random forest tree (RF) and support vector machine (SVM) model to screen hub ferroptosis genes (DE-FRGs). We used consistent unsupervised consensus clustering to cluster DKD samples, and enrichment analysis was performed by Gene Set Variation Analysis (GSVA), Gene Ontology (GO), and Kyoto Encyclopedia of Genes and Genomes (KEGG) and then assessed immune cell infiltration abundance using the single-sample gene set enrichment analysis (ssGSEA) and CIBERSORT algorithms. Ferroptosis scoring system was established based on the Boruta algorithm, and then, core compounds were screened, and binding sites were predicted by Coremine Medical database. Results We finally established a 7-gene signature (DUSP1, PRDX6, PEBP1, ZFP36, GABARAPL1, TSC22D3, and RGS4) that exhibited good stability across different datasets. Consistent clustering analysis divided the DKD samples into two ferroptosis modification patterns. Meanwhile, autophagy and peroxisome pathways and immune-related pathways can participate in the regulation of ferroptosis modification patterns. The abundance of immune cell infiltration differs significantly across patterns. Further, molecular docking results showed that the core compound could bind to the protein encoded by the core gene. Conclusions Our findings suggest that ferroptosis modification plays a crucial role in the diversity and complexity of the DKD immune microenvironment, and the ferroptosis score system can be used to effectively verify the relationship between ferroptosis and immune cell infiltration in DKD patients. Kaempferol and quercetin may be potential drugs to improve the immune and inflammatory mechanisms of DKD by affecting ferroptosis.
Research on a family of n-scroll chaos generators

This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions.
Albert algebras over rings and related torsors

Abstract We study exceptional Jordan algebras and related exceptional group schemes over commutative rings from a geometric point of view, using appropriate torsors to parametrize and explain classical and new constructions, and proving that over rings, they give rise to nonisomorphic structures. We begin by showing that isotopes of Albert algebras are obtained as twists by a certain $\mathrm F_4$ -torsor with total space a group of type $\mathrm E_6$ and, using this, that Albert algebras over rings in general admit nonisomorphic isotopes even in the split case, as opposed to the situation over fields. We then consider certain $\mathrm D_4$ -torsors constructed from reduced Albert algebras, and show how these give rise to a class of generalised reduced Albert algebras constructed from compositions of quadratic forms. Showing that this torsor is nontrivial, we conclude that the Albert algebra does not uniquely determine the underlying composition, even in the split case. In a similar vein, we show that a given reduced Albert algebra can admit two coordinate algebras which are nonisomorphic and have nonisometric quadratic forms, contrary, in a strong sense, to the case over fields, established by Albert and Jacobson.
One-dimensional system arising in stochastic gradient descent

Abstract We consider stochastic differential equations of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$, where f(x) behaves comparably to $|x|^k$ in a neighborhood of the origin, for $k\in [1,\infty)$. We show that there exists a threshold value $ \,{:}\,{\raise-1.5pt{=}}\, \tilde{\gamma}$ for $\gamma$, depending on k, such that if $\gamma \in (1/2, \tilde{\gamma})$, then $\mathbb{P}(X_t\rightarrow 0) = 0$, and for the rest of the permissible values of $\gamma$, $\mathbb{P}(X_t\rightarrow 0)>0$. These results extend to discrete processes that satisfy $X_{n+1}-X_n = f(X_n)/n^\gamma +Y_n/n^\gamma$. Here, $Y_{n+1}$ are martingale differences that are almost surely bounded. This result shows that for a function F whose second derivative at degenerate saddle points is of polynomial order, it is always possible to escape saddle points via the iteration $X_{n+1}-X_n =F'(X_n)/n^\gamma +Y_n/n^\gamma$ for a suitable choice of $\gamma$.
A hybrid Benders decomposition and bees algorithm matheuristic approach to transmission expansion planning considering energy storage

This paper introduces a novel hybrid optimisation algorithm that combines elements of both metaheuristic search and integer programming. This new matheuristic combines elements of Benders decomposition and the Bees Algorithm, to create the Bee-Benders Hybrid Algorithm (BBHA) which retains many of the advantages both of the methods. Specifically it is designed to be easily parallelizable, to produce good solutions quickly while still retaining a guarantee of optimality when run for a sufficiently long time. The algorithm is tested using a transmission network expansion and energy storage planning model, a challenging and very large scale mixed integer linear programming problem. Transmission network planning problems are already difficult on their own. When including the planning for storage systems in the network, the variation of demand over time has to be taken into account significantly increasing the size and difficulty of the optimization problem. The BBHA is shown to be highly effective hybrid matheuristic algorithm that performs at least as well as either Benders decomposition or the Bees Algorithm where these are effective on their own, and significantly improves upon the individual approaches where neither component part has a pronounced advantage. While the paper demonstrates the effectiveness in terms of the concrete electricity network planning problem, the algorithm could be readily applied to any mixed integer linear program, and is expected to work particularly well whenever this has a structure that is amenable to Benders decomposition.
Rayleigh and Brillouin modes in electrostrictive gratings

The formation of electrostrictive gratings in fluids is calculated by inclusion of viscosity and heat transfer. The reflectivity of the grating performs a damped oscillation with alternately higher and lower maxima. The normalized difference in height is determined by the thermal conductivity of the medium. Measurements have been performed for argon and nitrogen and are compared with the theory. Furthermore, the combined effect of electrostriction and radiative absorption is discussed.
On ideals of Ap with bounded approximate units and certain conditional expectations

Keywords: abelian locally compact group ; amenable locally compact ; group ; closed normal subgroup ; closed ideals ; Figa-Talamanca Herz algebra ; $p$- pseudomeasures ; conditional expectation ; approximate units Reference CAHRU-ARTICLE-1993-001doi:10.1112/jlms/s2-47.3. 497 Record created on 2008-12-10, modified on 2016-08-08
Sensing and mis‐sensing the eclipse

Morton, F. I. (1984) What are the limits on forest evaporation? J. Hydrol. , 14, pp. 373-398 (1985) What are the limits on forest evaporation? Reply. J. Hydrol. , 82, pp. 184-1 92 Verdecchia, M. , Visconti, G. , Giorgi, F. and Marinucci, M. R. (1994) Diurnal temperature range for a double carbon dioxide concentration experiment: analysis of possible physical mechanisms. Geophys. Res. Lett. , 21, pp. 1527-1530 and night-time temperatures. Weather, 53, pp. 7278 Mayes, J. and Sutton, G. (1997) Eastern England. In: Wheeler, D. and Mayes, J. (Eds.) Regional climates of the British Isles. Routledge, London, pp. 89-1 10 Monteith, J. L. (1999) Physical and physiological feedback constraining evaporation from land surfaces. In: Browning, K. A. and Gurney, R. J. (Eds.) Global energy and water cycles. Cambridge University Press, pp. 155-160 Monteith, J. L. and Unsworth, M. H. (1990) 1%ciples of environmental physics. Edward Arnold, Correspondence to: Dr J. G. Lockwood, 4 London Woodthorne Croft, Leeds LS 17 8XQ.
Compactifications of manifolds with boundary

This paper is concerned with compactifications of high-dimensional manifolds. Siebenmann’s iconic 1965 dissertation [L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, Ph.D. thesis, Princeton Univ. (1965), MR 2615648] provided necessary and sufficient conditions for an open manifold [Formula: see text] ([Formula: see text]) to be compactifiable by addition of a manifold boundary. His theorem extends easily to cases where [Formula: see text] is noncompact with compact boundary; however, when [Formula: see text] is noncompact, the situation is more complicated. The goal becomes a “completion” of [Formula: see text], i.e. a compact manifold [Formula: see text] containing a compactum [Formula: see text] such that [Formula: see text]. Siebenmann did some initial work on this topic, and O’Brien [G. O’Brien, The missing boundary problem for smooth manifolds of dimension greater than or equal to six, Topology Appl. 16 (1983) 303–324, MR 722123] extended that work to an important special case. But, until now, a complete characterization had yet to emerge. Here, we provide such a characterization. Our second main theorem involves [Formula: see text]-compactifications. An important open question asks whether a well-known set of conditions laid out by Chapman and Siebenmann [T. A. Chapman and L. C. Siebenmann, Finding a boundary for a Hilbert cube manifold, Acta Math. 137 (1976) 171–208, MR 0425973] guarantee [Formula: see text]-compactifiability for a manifold [Formula: see text]. We cannot answer that question, but we do show that those conditions are satisfied if and only if [Formula: see text] is [Formula: see text]-compactifiable. A key ingredient in our proof is the above Manifold Completion Theorem — an application that partly explains our current interest in that topic, and also illustrates the utility of the [Formula: see text]-condition found in that theorem.
Event-triggered damping stabilization of a linear wave equation.

The paper addresses the design of an event-triggering mechanism for a partial differential wave equation posed in a bounded domain. The wave equation is supposed to be controlled through a first order time derivative term distributed in the whole domain. Sufficient conditions based on the use of suitable Lyapunov functional are proposed to guarantee that an event-triggered distributed control still ensures the exponential stability of the closed-loop system. Moreover, the designed event-triggering mechanism allows to avoid the Zeno behavior. The 'existence and regularity' prerequisite properties of solutions for the closed loop system are also proven.
HARMONIC ANALYSIS OF ITERATED FUNCTION SYSTEMS WITH OVERLAP

An iterated function system (IFS) is a system of contractive mappings τi:Y→Y, i=1,…,N (finite), where Y is a complete metric space. Every such IFS has a unique (up to scale) equilibrium measure (also called the Hutchinson measure μ), and we study the Hilbert space L2(μ). In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory and from subband filter operators in signal processing. These Cuntz-like operator systems were used in recent papers on wavelet analysis by Baggett, Jorgensen, Merrill, and Packer [Contemp. Math. 345, 11–25 (2004)], where they serve as a first step to generating wavelet bases of Parseval type (alias normalized tight frames), i.e., wavelet bases with redundancy. Similarly, it was shown in work by Dutkay and Jorgensen [Rev. Mat. Iberoam. 22, 131–180 (2006)] that the iterative operator approach works well for generating wavelets on fractals from IFSs without overla.
Electroluminescence from lattice defects of photonic crystal slabs in blue-light-emitting diodes

Lattice defect structures embedded into perfect photonic crystal slabs have been fabricated onto the GaN surfaces of InGaN/GaN multi-quantum-well light-emitting diodes. The photonic crystal slab with a triangular lattice constant of 230 nm showed suppressed light extraction for the electroluminescence at a peak of 464 nm, but the light radiated through lattice defects. The perfect photonic crystal slab shows the cooperative phenomenon of a light scattering similar to Wood’s anomaly in a metallic grating, and lattice defects result in the leaky modes of light extractions by breaking the symmetry of cooperative light scattering.
Large-Scale Structure of the June–July 1996 Marine Boundary Layer along California and Oregon

Abstract Data from surface stations, profilers, long-range aircraft surveys, and satellites were used to characterize the large-scale structure of the marine boundary layer off of California and Oregon during June and July 1996. To supplement these observations, June–July 1996 averages of meteorological fields from the U.S. Navy’s operational Coupled Ocean–Atmospheric Mesoscale Prediction System (COAMPS) model were generated for the region. Model calculations show a broad band of fast northerly surface winds exceeding 7 m s−1 extending along the California–Oregon coast. Buoy-measured peaks of 7.1 m s−1 off Bodega Bay, 7.2 m s−1 off Point Piedras Blancas, and 8.8 m s−1 near Point Conception were reported. Mean winds at the buoys located 15–25 km offshore are generally faster than those at coastal stations, and all station winds are faster in the afternoon. The aircraft and station observations confirm that an air temperature inversion typically marks the top of the marine boundary layer, which deepens offs.