28,792 research outputs found

    Solutions to Landau equation under Prodi-Serrin's like criteria

    Full text link
    In this paper, we introduce Prodi-Serrin like criteria for weak solutions under which it is possible to show existence of classical solutions to the spatially homogeneous Landau equation for all classical potentials and dimensions d3d \ge 3. The physical case of Coulomb interaction in dimension d=3d=3 is included in our analysis, which generalizes the work of \cite{silvestre}. The first step consists in establishing instantaneous appearance of LpL^{p} estimates using the Prodi-Serrin criteria. Then, we introduce a new LpL^{p} to LL^{\infty} framework, using a suitable De Giorgi's argument reminiscent of the one found in \cite{ricardo}, which provides appearance of pointwise bounds for such solutions. Our approach is quantitative and does not require a preliminary knowledge of elaborate tools for nonlinear parabolic equations

    SignReLU neural network and its approximation ability

    Full text link
    Deep neural networks (DNNs) have garnered significant attention in various fields of science and technology in recent years. Activation functions define how neurons in DNNs process incoming signals for them. They are essential for learning non-linear transformations and for performing diverse computations among successive neuron layers. In the last few years, researchers have investigated the approximation ability of DNNs to explain their power and success. In this paper, we explore the approximation ability of DNNs using a different activation function, called SignReLU. Our theoretical results demonstrate that SignReLU networks outperform rational and ReLU networks in terms of approximation performance. Numerical experiments are conducted comparing SignReLU with the existing activations such as ReLU, Leaky ReLU, and ELU, which illustrate the competitive practical performance of SignReLU

    On a chemotaxis-hapotaxis model with nonlinear diffusion modelling multiple sclerosis

    Full text link
    We investigated existence of global weak solutions for a system of chemotaxis-hapotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of macrophages (mm), cytokine (cc) and apoptotic oligodendrocytes (dd). The main novelty in our work is the presence of a nonlinear diffusivity D(m)D(m), which results to be more appropriate from the modelling point of view. Under suitable assumptions and for sufficiently regular initial data, adapting the strategy in [30,44], we show the existence of global bounded solutions for the model analysed

    PROSIDING KONFERENSI NASIONAL ADMINISTRASI NEGARA SINAGARA 2020

    Get PDF
    PROSIDING KONFERENSI NASIONAL ADMINISTRASI NEGARASINAGARA 202

    Evaluasi Program Planing PLP II (Pengenalan Lapangan Persekolahan) : Menggunakan Model CSE-UCLA di PAUD

    No full text
    Artikel ini bertujuan untuk mendeskripsikan dan menganalisis kesesuaian komponen program planing meliputi: kemampuan dosen pembimbing dalam membimbing mahasiswa PLP II, kemampuan guru pamong dalam membimbing mahasiswa PLP II. Dalam studi evaluasi ini, penulis menggunakan model evaluasi yang dikembangkan oleh Alkin, yaitu model CSE-UCLA. Model CSE-UCLA terdiri atas 5 tahap evaluasi: 1) system assessment, 2) program planing, 3) program implementation, 4) program improvement, dan 5) program certification. Namun dalam artikel ini penulis hanya melihat satu komponen evaluasi yaitu: program planing. Penelitian evaluasi ini dilaksanakan di IAIN Kendari, dan tempat pelaksanaan PLP II mahasiswa Program Studi PIAUD FTIK IAIN Kendari di TK Sultan Qaimuddin Kendari pada tahun 2022. Informan penelitian terdiri dari dosen pembimbing, guru pamong dan mahasiswa PLP II. Hasil penelitian pada komponen evaluasi program planning, aspek yang dievaluasi meliputi aspek kemampuan dosen pembimbing dan kemampuan guru pamong PLP II. Temuan pertama pada kemampuan dosen pembimbing data yang diperoleh baik melalui wawancara, data angket menunjukan tingkat kemampuan dosen pembimbing dalam membimbing mahasiswa berada pada kategori tinggi. Kedua, pada aspek kemampuan guru pamong dalam membimbing mahasiswa PLP II menunjukan kategori tinggi

    Eigenvalue for a problem involving the fractional (p,q)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth

    Full text link
    In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional (p,q)(p,q)-Laplacian. The nonlinearity considered involves supercritical Sobolev growth. Our approach is variational togheter with the sub- and supesolution methods, and in this way we can address a wide range of problems not yet contained in the literature. Even when W0s1,p(Ω)L(Ω)W^{s_1,p}_0(\Omega) \hookrightarrow L^{\infty}\left(\Omega\right) failing, we establish uL(Ω)C[u]s1,p\|u\|_{L^{\infty}\left(\Omega\right)} \leq C[u]_{s_1,p} (for some C>0C>0 ), when uu is a solution

    Contribution of the Learning Model as a Provision for the Introduction of the School Field (PLP) to Optimize the Learning Process

    Get PDF
    Effective learning is an important aspect for students as a provision for the introduction of field schooling (PLP) for students. The purpose of this study was to determine how much students can apply effective learning models in the learning process when following PLP, as well as how the application of these models affect the effectiveness of learning when following PLP. The design of research conducted in this study is qualitative research with descriptive approach. The population in this study as many as 55 students and then sampled a number of 30 students with random sampling. The results of the observation sheet showed that most students (70%) can apply effective learning models in the learning process when following PLP. While the other 30% still have difficulty in implementing the model. The results of data reduction from interview sheets showed that most students (80%) stated that the application of effective learning models in PLP makes learning more fun and effective. Another 20% stated that they had difficulties in implementing the model. The results of data reduction from the questionnaire showed that most students choose expository learning (20%) Problem-Based (60%) and cooperative learning (15%), most students can apply problem-based learning models in the learning process when attending PLP. This can be seen from the reduction of observation sheet data which shows that 70% of students can apply the model. The results of interviews and questionnaires also showed that most students stated that the application of effective learning models in PLP makes learning more fun and effective

    Biocompatible Lysine Protecting Groups for the Chemoenzymatic Synthesis of K48/K63 Heterotypic and Branched Ubiquitin Chains

    No full text
    The elucidation of emerging biological functions of heterotypic and branched ubiquitin (Ub) chains requires new strategies for their preparation with defined lengths and connectivity. While in vitro enzymatic assembly using expressed E1-activating and E2-conjugating enzymes can deliver homotypic chains, the synthesis of branched chains typically requires extensive mutations of lysines or other sequence modifications. The combination of K48- and K63-biased E2-conjugating enzymes and two new carbamate protecting groupspyridoxal 5′-phosphate (PLP)-cleavable aminobutanamide carbamate (Abac group) and periodate-cleavable aminobutanol carbamate (Aboc group)provides a strategy for the synthesis of heterotypic and branched Ub trimers, tetramers, and pentamers. The Abac- and Aboc-protected lysines are readily prepared and incorporated into synthetic ubiquitin monomers. As these masking groups contain a basic amine, they preserve the overall charge and properties of the Ub structure, facilitating folding and enzymatic conjugations. These protecting groups can be chemoselectively removed from folded Ub chains and monomers by buffered solutions of PLP or NaIO4. Through the incorporation of a cleavable C-terminal His-tag on the Ub acceptor, the entire process of chain building, iterative Abac deprotections, and global Aboc cleavage can be conducted on a resin support, obviating the need for handling and purification of the intermediate oligomers. Simple modulation of the Ub monomers affords various K48/K63 branched chains, including tetramers and pentamers not previously accessible by synthetic or biochemical methods

    Representation Learning With Hidden Unit Clustering For Low Resource Speech Applications

    Full text link
    The representation learning of speech, without textual resources, is an area of significant interest for many low resource speech applications. In this paper, we describe an approach to self-supervised representation learning from raw audio using a hidden unit clustering (HUC) framework. The input to the model consists of audio samples that are windowed and processed with 1-D convolutional layers. The learned "time-frequency" representations from the convolutional neural network (CNN) module are further processed with long short term memory (LSTM) layers which generate a contextual vector representation for every windowed segment. The HUC framework, allowing the categorization of the representations into a small number of phoneme-like units, is used to train the model for learning semantically rich speech representations. The targets consist of phoneme-like pseudo labels for each audio segment and these are generated with an iterative k-means algorithm. We explore techniques that improve the speaker invariance of the learned representations and illustrate the effectiveness of the proposed approach on two settings, i) completely unsupervised speech applications on the sub-tasks described as part of the ZeroSpeech 2021 challenge and ii) semi-supervised automatic speech recognition (ASR) applications on the TIMIT dataset and on the GramVaani challenge Hindi dataset. In these experiments, we achieve state-of-art results for various ZeroSpeech tasks. Further, on the ASR experiments, the HUC representations are shown to improve significantly over other established benchmarks based on Wav2vec, HuBERT and Best-RQ

    Harder's conjecture II

    Full text link
    Let ff be a primitive form of weight 2k+j22k+j-2 for SL2(Z)SL_2(Z), and let p\mathfrak p be a prime ideal of the Hecke field of ff. We denote by SPm(Z)SP_m(Z) the Siegel modular group of degree mm. Suppose that k0mod2, j0mod4k \equiv 0 \mod 2, \ j \equiv 0 \mod 4 and that p\mathfrak p divides the algebraic part of L(k+j,f)L(k+j,f). Put k=(k+j/2,k+j/2,j/2+4,j/2+4){\bf k}=(k+j/2,k+j/2,j/2+4,j/2+4). Then under certain mild conditions, we prove that there exists a Hecke eigenform FF in the space of modular forms of weight (k+j,k)(k+j,k) for SP2(Z)SP_2(Z) such that [I2(f)]k[I_2(f)]^{\bf k} is congruent to A4(I)(F)A^{(I)}_4(F) modulo p\mathfrak p. Here, [I2(f)]k[I_2(f)]^{\bf k} is the Klingen-Eisenstein lift of the Saito-Kurokawa lift I2(f)I_2(f) of ff to the space of modular forms of weight k{\bf k} for SP4(Z)SP_4(Z), and A4(I)(F)A^{(I)}_4(F) is a certain lift of FF to the space of cusp forms of weight k{\bf k} for SP4(Z)SP_4(Z). As an application, we prove Harder's conjecture on the congruence between the Hecke eigenvalues of FF and some quantities related to the Hecke eigenvalues of ff
    corecore