Part I. Entire Functions of Finite Order: Growth of entire functions Main integral formulas for functions analytic in a disk Some applications of the Jensen formula Factorization of entire functions of finite order The connection between the growth of an entire function and the distribution of its zeros Theorems of Phragmen and Lindelof Subharmonic functions The indicator function The Polya Theorem Applications of the Polya Theorem Lower bounds for analytic and subharmonic functions Entire functions with zeros on a ray Entire functions with zeros on a ray (continuation) Part II. Entire Functions of Exponential Type: Integral representation of functions analytic in the half-plane The Hayman Theorem Functions of class $C$ and their applications Zeros of functions of class $C$ Completeness and minimality of system of exponential functions in $L^2(0,a)$ Interpolation by entire functions of exponential type Interpolation by entire functions of the spaces $L_\pi$ and $B_\pi$ Sin-type functions Riesz bases formed by exponential functions in $L^2(-\pi,\pi)$ Completeness of the eigenfunction system of a quadratic operator pencil Part III. Some Additional Problems of the Theory of Entire Functions: Carleman's and R. Nevanlinna's formulas and their applications Uniqueness problems for Fourier transforms and for infinitely-differentiable functions The Matsaev Theorem on the growth of entire functions admitting a lower bound Entire functions of the class $P$ S. N. Bernstein's inequality for entire functions of exponential type and its generalizations Bibliography Author index Subject index.
Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model $f(\mathbf{x})=\mathbf{x}^{T}β$ with a fixed coefficient vector $β$) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across all well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a single prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models.
Seismic waves have revealed that the oceanic plate beneath the Ontong Java Plateau was dramatically transformed by the colossal volcanic activity that created it more than 100 million years ago。 Researchers found a complex structure of horizontal layers cut through by vast swarms of vertical magma channels, along with unusually slow seismic waves s
Over the past few months, our team has been building more and more slidedecks using web frontend technologies with coding harnesses like Claude Code, but a common complaint is to make even small edits we need to edit the code either manually or via the harness。To avoid this loop, I ended up creating Bento, a single HTML file with everything you nee
Abstract A model of pollen deposition on the surface of an entire basin is developed to estimate pollen source area, and results are compared with those for a point at the center of a basin (I. C. Prentice, 1985, Quaternary Research 23, 76-86; 1988, "Vegetation History," (pp. 17-42, Kluwer Academic). This model is more appropriate for approximating the source area of pollen in lake sediment, since mixing in lake water and focusing of sediment redistribute pollen originally deposited over the entire surface. In general, the pollen source radius for the entire basin surface is 10-30% smaller than the source radius for a point at the center; the difference in the source radius is more profound for heavier pollen types such as spruce and sugar maple than for lighter types such as oak and ragweed. The average pollen input to the entire surface is more strongly influenced by nearby pollen sources than pollen deposition at the center. The pollen record from a lake may therefore provide different spatial resolution than the record from a bog of similar radius.
The sequence determination of the entire genome of the Synechocystis sp. strain PCC6803 was completed. The total length of the genome finally confirmed was 3,573,470 bp, including the previously reported sequence of 1,003,450 bp from map position 64% to 92% of the genome. The entire sequence was assembled from the sequences of the physical map-based contigs of cosmid clones and of lambda clones and long PCR products which were used for gap-filling. The accuracy of the sequence was guaranteed by analysis of both strands of DNA through the entire genome. The authenticity of the assembled sequence was supported by restriction analysis of long PCR products, which were directly amplified from the genomic DNA using the assembled sequence data. To predict the potential protein-coding regions, analysis of open reading frames (ORFs), analysis by the GeneMark program and similarity search to databases were performed. As a result, a total of 3,168 potential protein genes were assigned on the genome, in which 145 (4.6%) were identical to reported genes and 1,257 (39.6%) and 340 (10.8%) showed similarity to reported and hypothetical genes, respectively. The remaining 1,426 (45.0%) had no apparent similarity to any genes in databases. Among the potential protein genes assigned, 128 were related to the genes participating in photosynthetic reactions. The sum of the sequences coding for potential protein genes occupies 87% of the genome length. By adding rRNA and tRNA genes, therefore, the genome has a very compact arrangement of protein- and RNA-coding regions. A notable feature on the gene organization of the genome was that 99 ORFs, which showed similarity to transposase genes and could be classified into 6 groups, were found spread all over the genome, and at least 26 of them appeared to remain intact. The result implies that rearrangement of the genome occurred frequently during and after establishment of this species.
Here we demonstrate that the photoactivity of Au-decorated TiO2 electrodes for photoelectrochemical water oxidation can be effectively enhanced in the entire UV-visible region from 300 to 800 nm by manipulating the shape of the decorated Au nanostructures. The samples were prepared by carefully depositing Au nanoparticles (NPs), Au nanorods (NRs), and a mixture of Au NPs and NRs on the surface of TiO2 nanowire arrays. As compared with bare TiO2, Au NP-decorated TiO2 nanowire electrodes exhibited significantly enhanced photoactivity in both the UV and visible regions. For Au NR-decorated TiO2 electrodes, the photoactivity enhancement was, however, observed in the visible region only, with the largest photocurrent generation achieved at 710 nm. Significantly, TiO2 nanowires deposited with a mixture of Au NPs and NRs showed enhanced photoactivity in the entire UV-visible region. Monochromatic incident photon-to-electron conversion efficiency measurements indicated that excitation of surface plasmon resonance of Au is responsible for the enhanced photoactivity of Au nanostructure-decorated TiO2 nanowires. Photovoltage experiment showed that the enhanced photoactivity of Au NP-decorated TiO2 in the UV region was attributable to the effective surface passivation of Au NPs. Furthermore, 3D finite-difference time domain simulation was performed to investigate the electrical field amplification at the interface between Au nanostructures and TiO2 upon SPR excitation. The results suggested that the enhanced photoactivity of Au NP-decorated TiO2 in the UV region was partially due to the increased optical absorption of TiO2 associated with SPR electrical field amplification. The current study could provide a new paradigm for designing plasmonic metal/semiconductor composite systems to effectively harvest the entire UV-visible light for solar fuel production.
Scientists have found a way to revive vancomycin, a powerful antibiotic that some dangerous bacteria have learned to resist。 Instead of creating an entirely new drug, researchers paired vancomycin with a small molecule called pghi-4, which blocks a bacterial enzyme linked to resistance。 The combination restored the antibiotic’s ability to kill drug
Hi HN, We’re Adeel and Umair, co-founders of Unlayer (https://unlayer。 We let you add content creation to your applications without having to build an entire editor, renderer, template, and export stack yourself。 Unlayer lets you create emails, web pages, and documents inside your app, in three different ways: in code, visually, or with AI
Scientists have created a programmable optical chip that can slow light on demand, giving engineers far greater control over how optical signals propagate through a circuit。 The technology could provide the delays, synchronization, and buffering functions needed to make light-based computing more practical。 A single chip could eventually perform se
Scientists at Nanyang Technological University in Singapore have discovered a surprisingly simple way to create exotic light structures called optical skyrmions using a 200-year-old optical effect known as the Poisson spot。 Instead of relying on expensive, highly engineered materials, they simply shine a laser at a tiny circular disc, producing sta
Researchers have achieved a major milestone by creating a long-sought two-dimensional quantum material and confirming its unusual conducting edge states。 The ability to control these states through strain could make the material a promising platform for future room-temperature quantum electronics
A quantum problem once described as impossible for classical computers has now been solved using relatively modest hardware。 Researchers used tensor networks to compress the overwhelming wave function created by hundreds of entangled qubits, allowing some calculations to run on a laptop。 Their results matched both theoretical predictions and simula
NASA is ramping up its lunar ambitions by awarding nearly $600 million for four commercial Moon landings planned for late 2028。 Each mission will carry the same trio of science instruments to improve lunar navigation, study dangerous dust kicked up during landings, and map the Moon's radiation environment。 The agency also revealed plans for new rov
Dying Sun-like stars may not fade away quietly。 As blobs of gas erupt unevenly from their swollen surfaces, each burst gives the star a tiny push in the opposite direction。 Thousands of these random kicks could eventually break apart distant stellar pairs or, in rare cases, drive two stars into a violent collision
A new theoretical study offers a possible explanation for how the Universe can grow more complex without violating the second law of thermodynamics。 Using a quantum gravity framework called Gravity from Entropy, mathematician Ginestra Bianconi found that the Universe’s total entropy may rise as space expands, even while entropy within each unit of
Astronomers have found the first confirmed atmosphere around a rocky planet in another star’s habitable zone。 The planet, LHS 1140 b, revealed its atmosphere through helium slowly leaking into space。 Located 48 light-years away, the world may have preserved its atmosphere for billions of years, making it a promising target in the search for potenti