Jacobi fields in nonholonomic mechanics

In this paper, we define Jacobi fields for nonholonomic mechanics using a similar characterization than in Riemannian geometry. We give explicit conditions to find Jacobi fields and finally we find the nonholonomic Jacobi fields in two equivalent ways: the first one, using an appropriate complete lift of the nonholonomic system and, in the second one, using the curvature and torsion of the associated nonholonomic connection.

Stable Multi-Level Monotonic Eroders

Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.

On Baer cones in $$\mathrm {PG}(3, q)$$

Recently, in Innamorati and Zuanni (J. Geom 111:45, 2020. 10.1007/s00022-020-00557-0) the authors give a characterization of a Baer cone of $$\mathrm {PG}(3, q^2)$$ PG ( 3 , q 2 ) , q a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in $$q^2+1$$ q 2 + 1 , $$q^2+q+1$$ q 2 + q + 1 or $$q^3+q^2+1$$ q 3 + q 2 + 1 points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.

Modelling streamflow and sediment yield using Soil and Water Assessment Tool: A case study of Lidder watershed in Kashmir Himalayas, India

The conjunction of heavy snowfall during winters and intensive rainfall during monsoons along with the mountainous topography expose the Lidder watershed to serious erosion and flood aggravation issues. Barely any attempts have been made for an in-depth examination of Lidder watershed for precise estimation of sub-basin level runoff and erosion. In this study Soil and Water Assessment Tool (SWAT) was calibrated using Sequential Uncertainty Fitting algorithm (SUFI-2) for modelling streamflow and sediment yield of the Lidder watershed. Daily runoff and sediment event data from 2003–2013 were used in this study; data from 2003–2008 was used for calibration and 2009–2013 for validation. Model performance was evaluated using various statistical tools which showed good results revealing excellent potential of SWAT model to simulate streamflow and sediment yield for both calibration and validation periods. The annual rate of average upland sediment drawn from the watershed was approximately 853.96 Mg/ha for an average surface runoff of 394.15 mm/year. This study identifies the vulnerable areas of the Lidder watershed which can be thoroughly examined by decision-makers for effective management and planning. Further, the calibrated model can be applied to other watersheds with similar characterization to influence strategies in the management of watershed processes.

Existence and Convergence of Solutions to Fractional Pure Critical Exponent Problems

We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical exponent problem ( - Δ ) s ⁢ u s = | u s | 2 s ⋆ - 2 ⁢ u s , u s ∈ D 0 s ⁢ ( Ω ) , 2 s ⋆ := 2 ⁢ N N - 2 ⁢ s , (-\Delta)^{s}u_{s}=\lvert u_{s}\rvert^{2_{s}^{\star}-2}u_{s},\quad u_{s}\in D^% {s}_{0}(\Omega),\,2^{\star}_{s}:=\frac{2N}{N-2s}, where s is any positive number, Ω is either ℝ N {\mathbb{R}^{N}} or a smooth symmetric bounded domain, and D 0 s ⁢ ( Ω ) {D^{s}_{0}(\Omega)} is the homogeneous Sobolev space. Depending on the kind of symmetry considered, solutions can be sign-changing. We show that, up to a subsequence, a l.e.s.s. u s {u_{s}} converges to a l.e.s.s. u t {u_{t}} as s goes to any t > 0 {t>0} . In bounded domains, this convergence can be characterized in terms of an homogeneous fractional norm of order t - ε {t-\varepsilon} . A similar characterization is no longer possible in unbounded domains due to scaling invariance and an incompatibility with the functional spaces; to circumvent these difficulties, we use a suitable rescaling and characterize the convergence via cut-off functions. If t is an integer, then these results describe in a precise way the nonlocal-to-local transition. Finally, we also include a nonexistence result of nontrivial nonnegative solutions in a ball for any s > 1 {s>1} .

Characterization of the gut microbiota in diabetes mellitus II patients with adequate and inadequate metabolic control

Objective The objective of this study was to characterize the composition of the gut microbiota in type 2 Diabetes Mellitus (T2DM) patients with adequate and inadequate metabolic control, and its relationship with fiber consumption. Results A total of 26 patients with type 2 diabetes mellitus (T2DM) were enrolled, of which 7 (26.9%) cases had adequate metabolic control (HbA1c < 7%) and 19 (73.1%) inadequate metabolic control (HbA1c ≥ 7%). It was observed that among patients with controlled T2DM, 2 (28.6%) cases presented good intake of fiber and 5 (71.4%) cases a regular intake. In contrast, in patients with uncontrolled T2DM, 13 (68.4%) patients reported a regular intake and 6 (31.6%) a poor intake. In relation to the identification of the gut microbiota, both groups presented a similar characterization. There were differences in the population of bacteria identified in both groups, however, the results were not statistically significant. The most frequently identified bacteria in controlled and uncontrolled T2DM patients were Prevotella (71.4% vs 52.6%), followed by Firmicutes (71.4% vs 42.1%), Proteobacteria (71.4% vs 36.8%) and Bacteroidetes (57.1% vs 37.8%). On the other hand, Fusobacterium, Actinobacteria were not identified in either of the two groups of study.

Towards an Alternative to Time of Flight Diffraction Using Instantaneous Phase Coherence Imaging for Characterization of Crack-Like Defects

Time of flight diffraction (TOFD) is considered a reliable non-destructive testing method for the inspection of welds using a pair of single-element probes. On the other hand, ultrasonic phased array imaging has been continuously developed over the last couple of decades, and now features powerful algorithms, such as the total focusing method (TFM) and its multi-view approach to rendering detailed images of inspected parts. This article focuses on a different implementation of the TFM algorithm, relying on the coherent summation of the instantaneous signal phase. This approach presents a wide range of benefits, such as removing the need for calibration, and is highly sensitive to defect tips. This study compares the sizing and localization capabilities of the proposed method with the well-known TOFD. Both instantaneous phase algorithm and TOFD do not take advantage of the signal amplitude. Experimental tests were performed on a ¾″-thick steel sample with crack-like defects at different angles. Phase-based imaging techniques showed similar characterization capabilities as the standard TOFD method. However, the proposed method adds the benefit of generating an easy-to-interpret image that can help in localizing the defect. These results pave the way for a new characterization approach, especially in the field of automated ultrasonic testing (AUT).

On the spectrality of self-affine measures with four digits on ℝ2

In this paper, we study the spectral property of the self-affine measure [Formula: see text] generated by an expanding real matrix [Formula: see text] and the four-element digit set [Formula: see text]. We show that [Formula: see text] is a spectral measure, i.e. there exists a discrete set [Formula: see text] such that the collection of exponential functions [Formula: see text] forms an orthonormal basis for [Formula: see text], if and only if [Formula: see text] for some [Formula: see text]. A similar characterization for Bernoulli convolution is provided by Dai [X.-R. Dai, When does a Bernoulli convolution admit a spectrum? Adv. Math. 231(3) (2012) 1681–1693], over which [Formula: see text]. Furthermore, we provide an equivalent characterization for the maximal bi-zero set of [Formula: see text] by extending the concept of tree-mapping in [X.-R. Dai, X.-G. He and C. K. Lai, Spectral property of Cantor measures with consecutive digits, Adv. Math. 242 (2013) 187–208]. We also extend these results to the more general self-affine measures.

A geometric characterization of VES and Kadiyala-type production functions

The basic concepts of the differential geometry are shortly reviewed and applied to the study of VES production function in the spirit of the works of V?lcu and collaborators. A similar characterization is given for a more general production function, namely the Kadiyala production function, in the case of developable surfaces.

KARAKTERISASI CHITOSAN DAN CHITOSAN POLYMER MEDIUM DARI CANGKANG KEPITING BATU

Kepiting batu (Grapsus albolineatus) merupakan spesies yang banyak ditemukan di pantai berbatu dan eksoskeletonnya adalah salah sumber potensial chitin-chitosan. Chitosan adalah polimer bersifat polikationik dengan chitosan polymer medium (CPM) yang memiliki molekul lebih sederhana sebagai salah satu turunannya. Tujuan penelitian ini adalah untuk menentukan mutu chitosan dan chitosan polymer medium dari cangkang kepiting batu. Metode yang digunakan pada penelitian ini adalah metode eksperimental. Hasil analisis membuktikan bahwa cangkang kepiting memiliki komposisi 4.17±0.08 air, 54.4±2.78 abu, 6.28±0.05 lemak, 23.48±0.01 protein, 11.70±2.93 kaborhidrat. Karakterisasi chitosan memperlihatkan rendemen sebesar 10±0.70%, kadar air 8.10±0.14%, abu 19.39±0.55%, lemak 6.26±0.37%, protein 8.24±0.34%, karbodidrat 50.03±0.04%, derajat putih 60.61±0.86% , viscositas 7.30±0.42 cps dan derajat deasetilasi 55.92±1.30%. Untuk chitosan polymer medium, rendemennya mencapai 98.33±0.40% dan derajat deasetilasinya sebesar 60.22±0.24%. Chitosan dan chitosan polymer medium dari cangkang kepiting batu (Grapsus albolineatus) masih memenuhi standar yang ditetapkan SNI. Stone crab (Grapsus albolineatus) is a species commonly found in rocky beaches. Its exoskeleton is a good source of chitin and/or chitosan. Chitosan represents a polycationic polymer with chitosan polymer medium (CPM) having simpler molecular formula than chitosan as chitosan’s derivative. The objective of this research was to determine the quality of chitosan and chitosan polymer medium from rock crab’s shells. Experimental method was used in this study with characterization of the crab’s shells showing a composition of 4.17±0.08%, water, 54.4±2.78% ash, 6.28±0.05% fat, 23.48±0.01% protein and 11.70±2.93% carbohydrate. Similar characterization on chitosan revealed a composition of 10±0.70% rendemen, 8.10±0.14% water, 19.39±0.55% ash, 6.26±0.37% fat, 8.24±0.34% protein, 50.03±0.04% charabohydrate, 60.61±0.86% white degree, 7.30±0.42 cps viscosity and 55.92±1.30% degrees of deacetylation. Although chitosan contained similar composition of white degree (60%) and deactylation (60%0 to chitoxan polymer medium, CPM had higher composition of rendemen (98.33±0.40%) than chitosan (10±0.70%). In conclusion, this study shows that chitosan and chitosan polymer medium of G. albolineatus met our national standard (SNI).