Hausdorff dimension of the set of almost convergent sequences

The paper deals with the sets of numbers from [0,1] such that their binary representation is almost convergent. The aim of the study is to compute the Hausdorff dimensions of such sets. Previously, the results of this type were proved for a single summation method (e.g. Cesàro, Abel, Toeplitz). This study extends the results to a wide range of matrix summation methods.

Determining Suitable Locations for Regional Waste Final Processing Site (WFP) Using the Simple Additive Weighting (SAW) (Case Study: Malang City and Malang Regency)

Garbage or waste is basically a residual material resulting from human activities and natural processes that have no economic value anymore. The volume of waste in Malang City and Malang Regency every year always increases, so the existing waste final processing site will no longer be able to accommodate the pile of garbage. Therefore the Malang City Government plans to collaborate with the Malang Regency Government in making an integrated regional waste landfill and processing site. In this study, an analysis of the determination of the appropriate location for regional waste final processing for Malang City and Malang Regency was carried out using the Simple Additive Weighting (SAW) method. The SAW method is a weighted summation method, which can make a more precise assessment, based on the predetermined criteria and preference weights. Preference weights were determined by pairwise comparison method. The criteria used are geological hazardous areas, distance from drinking water sources, land slope level, distance from settlements, protected areas and distance from airports. The final result in this study is a map of the appropriate location for a regional waste final processing site and an analysis of the location for the best regional final processing site. The location map is classified into three, namely: not feasible with a total area of 54,774.33 ha, less feasible with a total area of 170,846.49 ha and feasible with a total area of 130,096.63 ha.

Overview in Summabilities: Summation Methods for Divergent Series, Ramanujan Summation and Fractional Finite Sums

This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent series. The first goal is to revisit the discussion about the existence of an algebraic constant related to a divergent series, which does not contradict the divergence of the series in the classical sense. The well-known Euler–Maclaurin summation formula is presented as an important tool. Throughout a systematic discussion, we seek to promote the Ramanujan summation method for divergent series and the methods recently developed for fractional finite sums.

Modeling and Analysis of Micro Surface Topography from Ball-End Milling in a Trochoidal Milling Mode

The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

Decay Heat Characterization for the European Sodium Fast Reactor

In this work a detailed assessment of the decay heat power for the commercial-size European Sodium-cooled Fast Reactor (ESFR) at the end of its equilibrium cycle has been performed. The summation method has been used to compute very accurate spatial- and time-dependent decay heat by employing state-of-the-art coupled transport-depletion computational codes and nuclear data. This detailed map provides basic information for subsequent transient calculations of the ESFR. A comprehensive analysis of the decay heat has been carried out and interdependencies among decay heat and different parameters characterizing the core state prior to shutdown, such as discharge burnup or type of fuel material, have been identified. That analysis has served as a basis to develop analytic functions to reconstruct the spatial-dependent decay heat power for the ESFR for cooling times within the first day after shutdown.

A compressed data approach for image-domain least-squares migration

We consider the problem of image-domain least-squares migration based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, where beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with non-negligible amplitudes need to be used to image the subsurface. In addition, due to the beams' spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix - an essential ingredient for least-squares migration. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

On efficient computation of sums of characters on the basis of A. G. Postnikov methods

An efficient p-adic method and the structure of an algorithm for computing the sums of characters of finite abelian groups are presented. The method and algorithm are based on the A.G. Postnikov summation method of characters modulo a prime power and its developments. A brief survey of the theory of characters of finite abelian groups, p-adic arithmetic and analysis is presented. Questions of the efficiency of p-adic methods are discussed. Moreover, we present results of computation of other types of sums of characters (Kloosterman sums), which are connecting with Artin-Schreier coverings over prime finite fields. The corresponding method and algorithm are based on the development of another method by A.G. Postnikov. Examples of computation of sums of characters are given.

Identification of Villages’ Development Types Using a Comprehensive Natural–Socioeconomic Framework

The establishment of a comprehensive framework to identify village development types is crucial to formulate plans for rural development and promote rural revitalization. This study proposed a natural–socioeconomic framework to identify the types of villages based on field survey, statistical data, and multi-source remote sensing images. The framework was constructed by combining the two-dimensional natural suitability/restriction evaluation and the four-dimensional socioeconomic development level evaluation. Then, the modified multiplication-weighted summation method and the coupling coordination degree algorithm were employed to identify the villages’ development types. A total of 774 villages of the Laiyang County, eastern China were used as the study areas to examine the framework. The results demonstrated the following. (1) There were 243,318 and 151 villages with high, moderate, low natural suitability, and 62 villages with natural restrictions; and 158,366 and 250 villages with high, moderate, and low economic development level, respectively. The distribution characteristic of natural evaluation was “high in the southwest and low in the northeast”, and the socioeconomic development level was generally centered on the urban area, which presented a “high–medium–low” circle-layer distribution structure. (2) There were 247 villages with high-level coupling coordination, 464 villages with intermediate coupling coordination, 1 village with low-level coupling coordination, and 62 villages with disordered coupling. (3) Based on the coupling coordination evaluation results, villages in the study area were grouped into five types: urbanization development (31%), construction development (16%), agglomeration linkage development (27%), decrease and improvement development (18%), and relocation and integration development (8%). The framework of villages’ development types identification established in this study can enrich the theory of rural geography, and the applied research results can provide a basis for rural revitalization and development planning.