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In this paper, we use concept of q-calculus and technique of convolution to study the q-Ruscheweyeh derivative by the concept of Janowski function, then we define new Subclass of analytic functions. Coefficients Estimates, radii of starlikeness, close to convexity, extreme points and many interesting properties are investigate, obtained and studied.

Solving partial differential equations (PDEs) is a fundamental problem in engineering and science. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is costly to obtain. Active Learning (AL) could help surrogate models reach the same accuracy with smaller training sets by querying classical solvers with more informative initial conditions and PDE parameters. While AL is more common in other domains, it has yet to be studied extensively for neural PDE solvers. To bridge this gap, we introduce AL4PDE, a modular and extensible active learning benchmark. It provides multiple parametric PDEs and state-of-the-art surrogate models for the solver-in-the-loop setting, enabling the evaluation of existing and the development of new AL methods for PDE solving. We use the benchmark to evaluate batch active learning algorithms such as uncertainty- and feature-based methods. We show that AL reduces the average error by up to 71% compared to random sampling and significantly reduces worst-case errors. Moreover, AL generates similar datasets across repeated runs, with consistent distributions over the PDE parameters and initial conditions. The acquired datasets are reusable, providing benefits for surrogate models not involved in the data generation., Comment: Code will be made available at https://github.com/dmusekamp/al4pde

In this study, we establish a significant connection between certain subclasses of complex order univalent functions and the Mittag-Leffler-type Poisson distribution series. We provide criteria for these series to belong to the specific subclasses. The primary goal of this investigation is to derive necessary and sufficient conditions for the Mittag-Leffler-type Poisson distribution series $\mathcal{P}(p,u,v)(z)$ to be included in the classes $\mathcal{S}(\delta,\eta,\tau)$ and $\mathcal{R}(\delta,\eta,\tau)$. These findings enhance our understanding of the structural properties of univalent functions and extend the applicability of Mittag-Leffler-type distributions in complex analysis.

Kernel orchestration is the task of mapping the computation defined in different operators of a deep neural network (DNN) to the execution of GPU kernels on modern hardware platforms. Prior approaches optimize kernel orchestration by greedily applying operator fusion, which fuses the computation of multiple operators into a single kernel, and miss a variety of optimization opportunities in kernel orchestration. This paper presents Korch, a tensor program optimizer that discovers optimal kernel orchestration strategies for tensor programs. Instead of directly fusing operators, Korch first applies operator fission to decompose tensor operators into a small set of basic tensor algebra primitives. This decomposition enables a diversity of fine-grained, inter-operator optimizations. Next, Korch optimizes kernel orchestration by formalizing it as a constrained optimization problem, leveraging an off-the-shelf binary linear programming solver to discover an optimal orchestration strategy, and generating an executable that can be directly deployed on modern GPU platforms. Evaluation on a variety of DNNs shows that Korch outperforms existing tensor program optimizers by up to 1.7x on V100 GPUs and up to 1.6x on A100 GPUs. Korch is publicly available at https://github.com/humuyan/Korch., Comment: Fix some typos in the ASPLOS version

Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity. Furthermore, all prevalent architectures for PDE solving lack at least one of several desirable properties of an ideal surrogate model, such as (i) generalization to PDE parameters not seen during training, (ii) spatial and temporal zero-shot super-resolution, (iii) continuous temporal extrapolation, (iv) support for 1D, 2D, and 3D PDEs, and (v) efficient inference for longer temporal rollouts. To address these limitations, we propose Vectorized Conditional Neural Fields (VCNeFs), which represent the solution of time-dependent PDEs as neural fields. Contrary to prior methods, however, VCNeFs compute, for a set of multiple spatio-temporal query points, their solutions in parallel and model their dependencies through attention mechanisms. Moreover, VCNeF can condition the neural field on both the initial conditions and the parameters of the PDEs. An extensive set of experiments demonstrates that VCNeFs are competitive with and often outperform existing ML-based surrogate models., Comment: Accepted for publication at the 41st International Conference on Machine Learning (ICML) 2024, Vienna, Austria; Project Page: https://jhagnberger.github.io/vectorized-conditional-neural-field/

Synthesis of transition metal oxides by microwave irradiation is a faster and energy-saving method compared to conventional heating in an electrical furnace because microwave energy is directly converted into heat within precursors. However, not much is known about how the physical properties are modified by the power of microwaves. We synthesized LaMnO3+d by irradiating oxide precursors with microwaves and studied the impact of microwave power (P = 1000 W, 1200 W, 1400 W and 1600 W) on magnetism, resistivity, magnetoresistance, thermopower, magnetic entropy change, magnetostriction, and electron spin resonance. It is found that paramagnetic to ferromagnetic transition becomes sharper, saturation magnetization increases, and electrical resistivity at low temperatures dramatically decreases as P increases. While the resistivity of samples irradiated with MW power of P less than or equal to 1400 W show insulating-like behavior down to 50 K, an insulator-metal transition occurs in the sample exposed to P = 1600 W and this sample also shows a maximum magnetoresistance (= -55%), magneto-thermopower (=-87%), magnetostriction (-180 x10-6) for H = 50 kOe and magnetic entropy change of 4.78 J/kg. K for H = 30 kOe around the Curie temperature. The intensity of electron spin resonance spectra at 300 K increases with P. We postulate that the much enhanced physical properties observed for the P = 1600 W sample arise from the creation of higher hole density, chemical homogeneity, and increased grain size. Our study shows that microwave power can be used as a knob to tune magnetism and other physical properties to our advantage., Comment: 17 pages, 5 figures