Miracle-dz/UniFAR-FTUs huggingface dataset:
Two-impurity Anderson model revisited: Competition between Kondo effect and reservoir-mediated superexchange in double quantum dots

We study a series-coupled double quantum dot in the Kondo regime modeled by the two-impurity Anderson model and find a new conduction-band mediated superexchange interaction that competes with Kondo physics in the strong Coulomb interaction limit. Our numerical renormalization group results, complemented with the higher-order Rayleigh-Schrodinger perturbation theory, show that the novel exchange mechanism leads to clear experimental consequences that can be checked in transport measurements through double quantum dots. PACS numbers: 73.21. La; 73.23. -b; 73.22. -f Quantum dots (QDs) (1) behave as quantum impurities, thus they exhibit the Kondo effect, the most spectacular man- ifestation of which is the transition from near-zero conduc - tance due to Coulomb blockade to perfect transmission (2, 3) as the temperature is lowered well below the Kondo tempera- ture, TK . More complex setups allow tailored realizations of strongly correlated electron systems in new situations. Dou- ble quantum dots (DQDs) (4, 5, 6, 7), for instance, are a minimal system for studying a lattice of magnetic impuri- ties in a tunable environment. In the two-impurity Kondo model, the competition between the Kondo effect and the anti- ferromagnetic (AF) interaction between impurities leads to a second-order quantum phase transition (QPT) (8). It is also known that the QPT is replaced by a crossover if electrons can tunnel between the impurities (9). In series-coupled DQDs, the most important contribution to the total AF exchange cou- pling is the superexchange coupling JU � 4t 2 =U , where t is the inter-dot hopping and U the on-site interaction. This superexchange vanishes (JU ! 0) as U ! 1 , which leads to the common belief (4, 7) that the Kondo physics always prevail in the large-U limit. In this Letter, we present numer- ical renormalization group (NRG) calculations which confute the above claim and unambiguously demonstrate the presence of a new type of spin-spin interaction which competes with Kondo physics in the large-U limit. Our main findings are illustrated in Fig. 4 where the peak position of the linear co n- ductance through a DQD versust exhibits a striking and unex- pected dependence on , the QD level broadening due to the coupling to the reservoir. Interestingly, the novel spin-s pin in- teraction reported here leads to observable experimental con- sequences like zero conductance G � 0 in regions where uni- tary transport G � 2e 2 =h is expected and vice versa. Intu- itively, we can understand this spin-spin interaction in te rms of virtual tunneling events involving conduction-band electrons; see Fig. 1. The strength of this spin-spin interaction, whic h we call conduction-band-mediated superexchange , JI , can be es- timated in the large-U limit using Rayleigh-Schrodinger per-
Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations

In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential equations of the type $du=(-\phi(-\Delta)u+f)dt +gdW_t$.
Exotic smoothings via large R⁴’s in Stein surfaces

We study the relationship between exotic R^4's and Stein surfaces as it applies to smoothing theory on more general open 4-manifolds. In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces. This relies on an extension of Casson's Embedding Theorem for locating Casson handles in closed 4-manifolds. Under sufficiently nice conditions, we show that using these R^4's as end-summands produces uncountably many diffeomorphism types while maintaining independent control over the genus-rank function and the Taylor invariant.
Cosmic ray current driven turbulence in shocks with efficient particle acceleration: the oblique, long-wavelength mode instability

In order for diffusive shock acceleration (DSA) to accelerate particles to high energies, the energetic particles must be able to interact with magnetic turbulence over a broad wavelength range. The weakly anisotropic distribution of accelerated particles, i.e. cosmic rays (CRs), is believed capable of producing this turbulence in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. In efficient DSA, this wave-particle interaction can be strongly non-linear where CRs modify the plasma flow and the specific mechanisms of magnetic field amplification. Resonant interactions have long been known to amplify magnetic fluctuations on the scale of the CR gyroradius, and Bell showed that the CR current can efficiently amplify magnetic fluctuations with scales smaller than the CR gyroradius. Here, we show with a multiscale, quasi-linear analysis that the presence of turbulence with scales shorter than the CR gyroradius enhances the growth of modes with scales longer than the gyroradius, at least for particular polarizations. We use a mean-field approach to average the equation of motion and the induction equation over the ensemble of magnetic field oscillations accounting for the anisotropy of relativistic particles on the background plasma. We derive the response of the magnetized CR current on magnetic field fluctuations and show that, in the presence of short-scale, Bell-type turbulence, long-wavelength modes are amplified. The polarization, helicity and angular dependence of the growth rates are calculated for obliquely propagating modes for wavelengths both below and above the CR mean free path. The long-wavelength growth rates we estimate for typical supernova remnant parameters are sufficiently fast to suggest a fundamental increase in the maximum CR energy that a given shock can produce.
UTILIZATION OF SCHOOLOGY: ITS RELATIONSHIP TO SELF-ASSESSMENT OF FIRST YEAR BEED STUDENTS

Central to this research is the utilization of Schoology as a learning modality and its relationship to self-assessment. This study employed the descriptive-correlational research design to determine the nature and magnitude by which these variables are related to each other. It included as respondents thirty first-year Bachelor of Elementary Education students who were enrolled in Notre Dame of Midsayap College during the second semester of Academic Year 2021-2022. Findings of the study revealed that the respondents had always utilized the learning management system (LMS) for uploading and notification, and monitoring and evaluation, and had oftentimes utilized it for activities and submission. However, they had only occasionally utilized it for the timely submission of their tasks. Meanwhile, the respondents were very good in performing their reflection papers, taking multiple choice types of exams and engaging in class discussions. Nevertheless, they were merely fair in doing poem/song compositions. Results bared that there is a moderately strong direct relationship between utilization of Schoology and self-assessment, and that relationship is highly significant, signifying that the LMS via Schoology had promoted effective learning among the respondents. Article visualizations:
A fixed point theorem for monotone asyptotic nonexpansive mappings

Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we establish an analogue to the original Goebel and Kirk's fixed point theorem for asymptotic nonexpansive mappings.
The existence of a giant cluster for percolation on large Crump–Mode–Jagers trees

Abstract In this paper we consider random trees associated with the genealogy of Crump–Mode–Jagers processes and perform Bernoulli bond-percolation whose parameter depends on the size of the tree. Our purpose is to show the existence of a giant percolation cluster for appropriate regimes as the size grows. We stress that the family trees of Crump–Mode–Jagers processes include random recursive trees, preferential attachment trees, binary search trees for which this question has been answered by Bertoin [7], as well as (more general) m-ary search trees, fragmentation trees, and median-of-( $2\ell+1$ ) binary search trees, to name a few, where to our knowledge percolation has not yet been studied.
Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization

Author(s): Davies, Frederick B; Furlanetto, Steven R | Abstract: Extremely large opaque troughs in the Lyman-alpha forest have been interpreted as a sign of an extended reionization process below z~6. Such features are impossible to reproduce with simple models of the intergalactic ionizing background that assume a uniform mean free path of ionizing photons. We build a self-consistent model of the ionizing background that includes fluctuations in the mean free path due to the varying strength of the ionizing background and large-scale density field. The dominant effect is the suppression of the ionizing background in large-scale voids due to "self-shielding" by an enhanced number of optically thick absorbers. Our model results in a distribution of 50 Mpc/h Lyman-alpha forest effective optical depths that significantly improves agreement with the observations at z~5.6. Extrapolation to z~5.4 and z~5.8 appears promising, but matching the mean background evolution requires evolution in the absorber population beyond the scope of the present model. We also demonstrate the need for extremely large volumes (g400 Mpc on a side) to accurately determine the incidence of rare large-scale features in the Lyman-alpha forest.
What is an answer? - remarks, results and problems on PIO formulas in combinatorial enumeration, part I

For enumerative problems, i.e. computable functions f from N to Z, we define the notion of an effective (or closed) formula. It is an algorithm computing f(n) in the number of steps that is polynomial in the combined size of the input n and the output f(n), both written in binary notation. We discuss many examples of enumerative problems for which such closed formulas are, or are not, known. These problems include (i) linear recurrence sequences and holonomic sequences, (ii) integer partitions, (iii) pattern-avoiding permutations, (iv) triangle-free graphs and (v) regular graphs. In part I we discuss problems (i) and (ii) and defer (iii)--(v) to part II. Besides other results, we prove here that every linear recurrence sequence of integers has an effective formula in our sense.
Problem based Learning: Its effect on problem solving skills of Islamic Boarding School student

Increasing problem-solving competence is fundamental for students to learn in the future. The application of problem-based learning (PBL) has not been optimal, especially in Islamic boarding schools. This study aims to know the effect of PBL learning model on problem-solving skills of students in Islamic boarding schools. The type of research used is quasi-experimental research. The populations in this study were 4 classes with a total of 108 students. The sample consisted of 2 classes, namely class X IPA A as the experimental class and class X IPA B as the control class, 26 students each. The sampling technique used cluster random sampling. Data collection techniques using test instruments in the form of multiple choice with 25 questions. The data analysis technique used in this study was the normality test, homogeneity test, and hypothesis testing. The results were tested using a paired sample test (t test) on the PBL learning model on problem-solving skills, the significant value was 0.000 (sig. <0.05) then H0 is rejected and Ha is accepted. These results indicate a significant difference using the PBL model compared to conventional learning. PBL is an alternative learning model that encourages student-oriented biological learning and improves students' ability to solve problems, especially in Islamic boarding schools.Abstrak Peningkatan kompetensi pemecahan masalah menjadi hal mendasar bagi siswa untuk belajar di masa depan. Penerapan pembelajaran berbasis masalah (PBL) belum optimal khususnya di Pesantren.Penelitian ini bertujuan untuk mengetahui pengaruh model pembelajaran PBL terhadap kemampuan memecahkan masalah pada siswa di pesantren. Jenis penelitian yang digunakan adalah penelitian eksperimen semu. Populasi dalam penelitian ini adalah 4 kelas dengan jumlah 108 siswa. Sampel terdiri atas 2 kelas yaitu kelas X IPA A sebagai kelas eksperimen dan kelas X IPA B sebagai kelas kontrol, masing-masing kelas terdiri atas 26 siswa. Teknik pengambilan sampel menggunakan cluster random sampling. Teknik pengumpulan data menggunakan instrumen tes berupa 25 soal pilihan berganda. Teknik analisis data penelitian ini menggunakan uji normalitas,uji homogenitas, dan uji hipotesis.Hasil penelitian diuji menggunakan paired sample test (uji t) pada model pembelajaran PBL terhadap kemampuan memecahkan masalah, diperoleh nilai signifikan 0,000 (sig.<0,05) maka H0 ditolak dan Ha diterima. Hasil tersebut menunjukkan adanya perbedaan signifikan dengan menggunakan model pembelajaran PBL dibandingkan dengan pembelajaran konvensional. PBL sebagai alternatif model pembelajaran yang mendorong pembelajaran biologi berorientasi siswa serta meningkatkan kemampuan siswa dalam memecahkan masalah khususnya pada siswa Pesantren.
Covering arrays from maximal sequences over finite fields

The focus of this thesis is the study and construction of covering arrays, relying on maximal period sequences and other tools from finite fields. A covering array of strength $t$, denoted $\mathrm{CA}(N; t, k,v)$, is an $N\times k$ array with entries from an alphabet $A$ of size $v$, with the property that in the $N\times t$ subarray defined by any $t$ columns, each of the $v^t$ vectors in $A^t$ appears at least once as a row. Covering arrays generalize orthogonal arrays, which are classic combinatorial objects that have been studied extensively. Constructing covering arrays with a small row-to-column ratio is important in the design of statistical experiments, however it is also a challenging mathematical problem. Linear feedback shift register (LFSR) sequences are sequences of elements from a finite field that satisfy a linear recurrence relation. It is well-known that these are periodic; LFSR sequences that attain the maximum possible period are maximal (period) sequences, often abbreviated to m-sequences in the literature. Arrays constructed from cyclic shifts of maximal sequences possess strong combinatorial properties and have been previously used to construct orthogonal and covering arrays (Moura et al., 2016), although only one of the known constructions is for covering arrays that are not orthogonal arrays (Raaphorst et al., 2014). In this thesis we present several new such constructions. The cornerstone of our results is a study of the combinatorial properties of arrays constructed from maximal sequences, where we make fundamental connections with concepts from diverse areas of discrete mathematics, such as orthogonal arrays, error-correcting codes, divisibility of polynomials and structures of finite geometry. One aspect of our work involves [. ]
A growth model in a random environment

We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height above $x-1$, if the latter height is larger; otherwise the height above $x$ increases by 1 with probability $p_x$. We assume that $p_x$ are chosen independently at random with a common distribution $F$, and that the initial state is such that the origin is far above the other sites. We explicitly identify the asymptotic shape and prove that, in the pure regime, the fluctuations about that shape, normalized by the square root of time, are asymptotically normal. This contrasts with the quenched version: conditioned on the environment, and normalized by the cube root of time, the fluctuations almost surely approach a distribution known from random matrix theory.
Topological d-wave pairing structures in Jain states

We discuss $d$-wave topological (broken time-reversal symmetry) pairing structures in unpolarized and polarized Jain states. We demonstrate pairing in the Jain spin-singlet state by rewriting it in an explicit pairing form, in which we can recognize $d$-wave weak pairing of underlying quasiparticles---composite fermions. We find and describe the root configuration of the Jain spin-singlet state and its connection with neutral excitations of the Haldane-Rezayi state, and study the transition between these states via exact diagonalization. We find high overlaps with the Jain spin-singlet state upon a departure from the hollow-core model for which the Haldane-Rezayi state is the exact ground state. Due to a proven algebraic identity we are able to extend the analysis of topological $d$-wave pairing structures to polarized Jain states and integer quantum Hall states and discuss its consequences.
A CHANDRA STUDY OF THE RADIO GALAXY NGC 326: WINGS, OUTBURST HISTORY, AND ACTIVE GALACTIC NUCLEUS FEEDBACK

NGC 326 is one of the most prominent “X”- or “Z”-shaped radio galaxies (XRGs/ZRGs) and has been the subject of several studies attempting to explain its morphology through either fluid motions or reorientation of the jet axis. We examine a 100 ks Chandra X-Ray Observatory exposure and find several features associated with the radio galaxy: a high-temperature front that may indicate a shock, high-temperature knots around the rim of the radio emission, and a cavity associated with the eastern wing of the radio galaxy. A reasonable interpretation of these features in light of the radio data allows us to reconstruct the history of the active galactic nucleus (AGN) outbursts. The active outburst was likely once a powerful radio source which has since decayed, and circumstantial evidence favors reorientation as the means to produce the wings. Because of the obvious interaction between the radio galaxy and the intracluster medium and the wide separation between the active lobes and wings, we conclude that XRGs are excellent sources in which to study AGN feedback in galaxy groups by measuring the heating rates associated with both active and passive heating mechanisms.
REDSHIFT EVOLUTION OF THE GALAXY VELOCITY DISPERSION FUNCTION

We present a study of the evolution of the galaxy velocity dispersion function (VDF) from z = 0 to z = 1.5 using photometric data from the Ultra-Deep and the NEWFIRM Medium-Band Survey in the COSMOS field. The VDF has been measured locally using direct kinematic measurements from the Sloan Digital Sky Survey (SDSS), but direct studies of the VDF at high redshift are difficult as they require velocity dispersion measurements of many thousands of galaxies. Taylor et al. demonstrated that dynamical and stellar masses are linearly related when the structure of the galaxy is accounted for. We show that the stellar mass, size, and Sérsic index can reliably predict the velocity dispersions of SDSS galaxies. We apply this relation to galaxies at high redshift and determine the evolution of the inferred VDF. We find that the VDF at z ∼ 0.5 is very similar to the VDF at z = 0. At higher redshifts, we find that the number density of galaxies with dispersions ≲ 200 km s−1 is lower, but the number of high-dispersion galaxies is constant or even higher. At fixed cumulative number density, the velocity dispersions of galaxies with log N[Mpc−3] < −3.5 increase with time by a factor of ∼1.4 from z ∼ 1.5–0, whereas the dispersions of galaxies with lower number density are approximately constant or decrease with time. The VDF appears to show less evolution than the stellar mass function, particularly at the lowest number densities. We note that these results are still somewhat uncertain and we suggest several avenues for further calibrating the inferred velocity dispersions.
THE MEDIATING EFFECT OF JOB SATISFACTION ON THE RELATIONSHIP BETWEEN TEAM WORK SKILLS AND WORK VALUES OF TEACHERS

The purpose of this study was to determine the mediating effect of job satisfaction on the relationship between teamwork skills and the work values of teachers. Utilizing quantitative, non-experimental design via correlational technique, data were obtained from 300 elementary public-school teachers who belong to the 3 districts, Magsaysay, Bansalan and Matan-ao under the Division of Davao Del Sur in the province of Davao Del Sur. The researcher utilized a stratified random sampling technique and an online survey mode of data collection. The researcher also utilized the statistical tools mean, Pearson r and Path Analysis. From the results of the study, it was found that there is a high level of mean scores for all variables of teamwork skills, work values and job satisfaction of teachers. Also, results revealed that there are significant relationships between teamwork skills and work values, between teamwork skills and job satisfaction and between job satisfaction and work values of teachers. Further, it was revealed that there was a full mediation effect of job satisfaction on the relationship between teamwork skills and the work values of teachers. This implies that teamwork skills convey the job satisfaction of teachers. Article visualizations:
Cartier modules and cyclotomic spectra

<p>We construct and study a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="t"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding="application/x-tex">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-structure on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="t"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding="application/x-tex">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-structure. Our main tool is a new approach to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-typical cyclotomic spectra via objects we call <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-typical topological Cartier modules. Using these, we prove that the heart of the cyclotomic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="t"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding="application/x-tex">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-structure is the full subcategory of derived <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper V"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding="application/x-tex">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-complete objects in the abelian category of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-typical Cartier modules. </p>