Small Order Research Articles

Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns.

We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which quantifies the regularity of the hyperuniform point patterns. The results are compared with those calculated with the conventional running average method. To discuss how the lattice symmetry affects the order metric, we treat the trellis and Shastry-Sutherland lattices with the same point density as examples of periodic lattices, and Stampfli hexagonal and dodecagonal quasiperiodic tilings with the same point density as examples of quasiperiodic tilings. It is found that the order metric for the Shastry-Sutherland lattice (Stampfli dodecagonal tilings) is smaller than the other in the periodic (quasiperiodic) tiling, meaning that the order metric is deeply related to the lattice symmetry. Namely, the point pattern with higher symmetry is characterized by the smaller order metric when their point densities are identical. Order metrics for several other quasiperiodic tilings are also calculated.

Bioluminescence in cephalopods: biodiversity, biogeography and research trends

Numerous terrestrial and marine organisms, including cephalopods, are capable of light emission. In addition to communication, bioluminescence is used for attraction and defense mechanisms. The present review aims to: (i) present updated information on the taxonomic diversity of luminous cephalopods and morphological features, (ii) describe large-scale biogeographic patterns, and (iii) show the research trends over the last 50 years on cephalopod bioluminescence. According to our database (834 species), 32% of all known cephalopod species can emit light, including oegopsid and myopsid squids, sepiolids, octopuses, and representatives of several other smaller orders (bathyteuthids, and the monotypic vampire “squid”, Vampyroteuthis infernalis and ram’s horn “squid”, Spirula spirula). Most species have a combination of photophores present in different locations, of which light organs on the head region are dominant, followed by photophores associated with the arms and tentacles and internal photophores. Regarding the biogeographic patterns of cephalopod species with light organs, the most diverse ocean is the Pacific Ocean, followed by the Atlantic and Indian Oceans. The least diverse are the Southern and the Arctic Oceans. Regarding publication trends, our systematic review revealed that, between 1971 and 2020, 277 peer-reviewed studies were published on bioluminescent cephalopods. Most research has been done on a single species, the Hawaiian bobtail squid Euprymna scolopes. The interest in this species is mostly due to its species-specific symbiotic relationship with the bacterium Vibrio fischeri, which is used as a model for the study of Eukaryote–Prokaryote symbiosis. Because there are many knowledge gaps about the biology and biogeography of light-producing cephalopods, new state-of-the-art techniques (e.g., eDNA for diversity research and monitoring) can help achieve a finer resolution on species’ distributions. Moreover, knowledge on the effects of climate change stressors on the bioluminescent processes is nonexistent. Future studies are needed to assess such impacts at different levels of biological organization, to describe the potential broad-scale biogeographic changes, and understand the implications for food web dynamics.

Coupled LQG with robust control for milling chatter suppression

This paper applies a coupled control method of LQG and robust to suppress milling chatter. With two controllers working together, the coupled control method has strong robustness to reject disturbances. According to this superiority, the time delay item caused by the regenerative effect is regarded as a disturbance for simplifying the system model. Thus the designed controller has a relatively smaller order than other time delay approximation or discretization methods. Based on the designed active control system, simulated results show the coupled control method has better performance than the original LQG and robust control methods. In experiments, the coupled control method improves the average critical cutting depth from 1.5 mm to 6 mm with almost the same control voltage as LQG and robust control methods, while they only improve the corresponding depth to 4.5 mm and 3.5 mm respectively. Furthermore, the stability improvement is also larger than a recently published control method used in milling chatter suppression. The largest stable milling region improvement among these methods shows potential of the coupled control method in milling chatter suppression.

Kinetic model for Pd-based membranes coking/deactivation in propane dehydrogenation processes

This work aims at providing insight into the deactivation mechanism of Pd-based membranes in propane dehydrogenation processes. Thermogravimetric analysis (TGA) experiments were conducted to study the adsorption and coking of propylene over conventional thin layer (TL) and double-skinned (DS) Pd-based membranes under several operating conditions. A mechanistic monolayer-multilayer coke growth model was selected to mathematically describe the membrane coking observed during TGA experiments. In addition, the reaction rate of coke formation and its influence on membranes deactivation has been studied. The deactivation model able to describe the hydrogen flux decay over time suggests that monolayer coke is the main responsible for the membrane deactivation. Multilayer coke also causes deactivation but with a smaller order than monolayer coke, for both the TL and the DS membranes. Among the two membrane types, DS membrane deactivates faster, i.e. with a higher order than the TL membrane, which is equal to 1.55 for the former and 0.51 for the latter. This is related to the higher number of active sites available in the controlling step of the deactivation reaction, which are most probably given by the addition of the ceramic Al2O3 protective layer. XPS spectra further confirms that, in the presence of Pd, Al2O3 sites contribute to carbon formation by evidencing a different nature of carbon formed on the two membranes. Finally, the experimental results of hydrogen permeation over time conducted on different membranes types and operative conditions confirmed the validity of the derived and parametrized kinetic models for coke formation and membrane deactivation. The experimental findings and the kinetic model derived in this work provide essential tools for the design and optimization of membrane reactors for dehydrogenation processes.

Orderings of extremes from dependent Gaussian variables with Archimedean copula under simple tree order restrictions

Suppose the random variables follow normal distributions , , and their dependence is modelled by Archimedean copula with generator ϕ. Then, the following results are established for the largest order statistics: (1) Suppose and are increasing in t>0, then, if and for we have ; (2) Suppose is decreasing and is increasing in t>0, then, if and for we have ; (3) Suppose and are increasing in t>0, then, if and for we have ; (4) Suppose is decreasing and is increasing in t>0, then, if and for we have . Analogous results are then established for smallest order statistics as well. In addition, we present some numerical examples to illustrate all the results established here. Finally, some concluding remarks are made.

Hand detection application based on QRD RLS lattice algorithm and its implementation on Xilinx Zynq Ultrascale+

The present paper describes hand detection application implemented on Xilinx Zynq Ultrascale+ device, comprising multi-core processor ARM Cortex A53 and FPGA programmable logic. It uses ultrasound data and is based on adaptive QRD RLS lattice algorithm extended with hypothesis testing. The algorithm chooses between two use-cases: (1) “there is a hand in front of the device” vs (2) “there is no hand in front of the device”. For these purposes a new structure of the identification models was designed. The model presenting use-case (1) is a regression model, which has the order sufficient to cover all incoming data. The model responsible for use-case (2) is a regression model, which has a smaller order than the model (1) and a certain time delay, covering the maximal distance where the hand can possibly appear. The offered concept was successfully verified using real ultrasound data in MATLAB optimized for parallel processing and implemented in parallel on four cores of ARM Cortex A53 processor. It was proved that computational time of the algorithm is sufficient for applications requiring real-time processing.

Stochastic comparisons of extreme order statistic from dependent and heterogeneous lower-truncated Weibull variables under Archimedean copula

<abstract><p>This article studies the stochastic comparisons of order statistics with dependent and heterogeneous lower-truncated Weibull samples under Archimedean copula. To begin, we obtain the usual stochastic and hazard rate orders of the largest and smallest order statistics from heterogeneous and dependent lower-truncated Weibull samples under Archimedean copula. Second, under Archimedean copula, we get the convex transform and the dispersive orders of the largest and smallest order statistics from dependent and heterogeneous lower-truncated Weibull samples. Finally, several numerical examples are given to demonstrate the theoretical conclusions.</p></abstract>

Ordering results of the smallest order statistics from independent heterogeneous new modified generalized linear failure rate random variables

This article deals with stochastic comparisons of series systems comprising a new modified generalized linear failure rate family of distributions. The results are established in three directions. First, we establish based on vector majorization the usual stochastic order and the hazard rate order of series systems. Next, multiple-outlier models are considered. When the number of components is equal, the results are obtained in terms of the likelihood ratio order. For an unequal number of components, we develop comparisons according to the usual stochastic order, and hazard rate order. Then, based on weak majorization and p-larger orders between the vector of parameters, some characterization results for comparing the lifetimes of series systems are also established. Finally, we discuss based on multivariate chain majorization the usual stochastic order of series systems. Numerical examples are considered to illustrate the results.

ON TIME SERIES MODEL ORDER SELECTION OF NON-STATIONARY AND NON-NORMAL DATA STRUCTURE

The study is aimed at identifying the orders of Time Series Models in Non-Stationarity Non-normal data structure from Uniform distributions with a view to determining the best Autoregressive/ Moving Average orders from time series models (ARMA and ARIMA) under different underline distributions when Non-Stationarity assumption is assumed. The data is generated from Autoregressive (AR) linear of second orders of general classes of Autoregressive functions. The generation of the data used for this simulation study is non-stationary cases and nonnormal. The data were simulated for both response variables and error terms from non-normal Distribution. The result shows that the values of the penalty function: AIC, BIC, HQIC and FPE of the order selection increases with increase in sample size but decreases with increasing order. It was observed that at both lower (20, 40) and larger (160,180 and 200) sample sizes, models with smallest orders. Similarly, the selection process is tied to the principle of parsimony i.e smaller orders are selected, but vary with the variation in the distribution of the series. The study recommends the need to develop a methodology for model selection combining objective and subjective techniques.

Spatial Rearrangement Using Pairwise Exchange Method (Case Study of PT. LMN)

PT. LMN is a company engaged in the manufacturing and outer production industry, the purpose of this research is to obtain a new layout design that can minimize the distance to move goods and the minimum total cost that can minimize the distance to move goods and the minimum total costs so as to reduce production costs, and obtain The new layout is better than the previous layout. Data processing begins by determining the initial sequence as a planning basis, then performing pairwise exchanges based on the initial sequence so as to produce several alternatives, do this stage until you get the smallest results. Lastly compares the new smallest order with the starting sequence. From the calculation, the results obtained are the proposed sequence (5 - 6 - 8 - 3 - 2 - 7 - 4 - 1 - 9) with a total value of 3450.5 meters. This proposal resulted in a total distance difference of 980.5 meters and a cost of IDR 11,736,8167 / per production. So that companies can reduce distance and also costs in each production process.

Functional observer design for nonlinear systems with incremental quadratic constraints

We present a functional observer design method for a class of nonlinear systems with output nonlinearities and incremental quadratic constraints. The system under consideration includes a wider class of nonlinear systems, such as, Lipschitz, one-sided Lipschitz, nondecreasing nonlinearity system as special cases. Based on Moore–Penrose pseudo-inverse and linear matrix inequality theory, the existence conditions of gain matrices of a functional observer are obtained. Moreover, exponential convergence of the estimate errors is achieved. Through the Lorenz system, it is shown that the proposed approach provides a smaller order of observer than that of the conventional approaches, while maintaining satisfactory performances.

Uniqueness Problems about Entire Functions with Their Difference Operator Sharing Sets

In this paper, we study the uniqueness questions of finite order transcendental entire functions and their difference operators sharing a set consisting of two distinct entire functions of finite smaller order. Our results in this paper improve the corresponding results from Liu (2009) and Li (2012).

Steklov spectral problems in a set with a thin toroidal hole

The paper concerns the Steklov spectral problem for the Laplace operator, and some variants in a 3-dimensional bounded domain, with a cavity Γ ε having the shape of a thin toroidal set, with a constant cross-section of diameter ε ≪ 1 . We construct the main terms of the asymptotic expansion of the eigenvalues in terms of real-analytic functions of the variable | ln ε | − 1 , and we prove that the relative asymptotic error is of much smaller order O ( ε | ln ε | ) as ε → 0 + . The asymptotic analysis involves eigenvalues and eigenfunctions of a certain integral operator on the smooth curve Γ , the axis of the cavity Γ ε .

Pole-Zero REM Modeling with Application in EEG Artifact Removal.

A new approach of pole-zero modeling in the presence of white noise is proposed. While the model estimate is calculated through the conventional least square estimation, the choice of number of poles and zeros in this scenario is critical and a challenging task. A wrong choice can overfit the additive noise in larger orders or underfit and discard parts of the noiseless data in smaller orders. To overcome this issue, we choose the order through RE Minimization (REM). RE is the error between the observed noisy data and the unavailable noiseless output. Using the available output error, the method provides a probabilistic worst case upperbound for RE and optimizes it. Simulation results on generated synthetic data show advantages of REM compared to existing order selection methods such as AIC and BIC. The results show that the proposed method avoids over or under parametrizing of AIC and BIC. The results in a practical application of EOG artifacts removal of eye blinks from EEG data provides an efficient modeling of the true background EEG with optimal eye blink removal.

A New Characterization of Hamilton Groups with the Smallest Order

Let G be a group and τe(G) the set of numbers of elements of G of the same order. In this paper, by τe(G), we get a new characterization of, where Q 8 is the Quaternion group of order 8. We get the theorem following: Theorem. Let G be a non-abelian group, G≅Q 8 if and only if τe(G) = τe(Q 8) = {1,6}.

Use of Haversine Formula in Finding Distance Between Temporary Shelter and Waste End Processing Sites

One way to handle waste of garbage problems can be done by determining the location of any Temporary Shelters that can be visited first. To determine this, it is necessary to find the distance between the location where the driver is located and which Temporary Shelter is available. This study aims to find the distance between the location of drivers and Temporary Shelters using the Haversine formula that can produce a distance between two points on the surface of the globe. The study was conducted by taking the location of drivers and Temporary Shelters in the form of coordinate points, calculating the distance between the points where drivers and Temporary Shelters are located, and comparing the results of distances obtained. The results of the study are a list of drivers and Temporary Shelters’ distances from the smallest order. With the selection of visits from the closest distance first, it is expected that drivers can save costs and travel time taken to visit all Temporary Shelters and end up at Waste End Processing Sites.

New type of gamma kernel density estimator

We discuss a new kernel type estimator for density function $$f_X(x)$$ with nonnegative support. Here, we use a type of gamma density as a kernel function and modify it with expansions of exponential and logarithmic functions. Our modified gamma kernel density estimator is not only free of the boundary bias, but the variance is also in smaller orders, which are $$O(n^{-1}h^{-1/4})$$ in the interior and $$O(n^{-1}h^{-3/4})$$ in the boundary region. Furthermore, the optimal orders of its mean squared error are $$O(n^{-8/9})$$ in the interior and $$O(n^{-8/11})$$ in the boundary region. Simulation results that demonstrate the proposed method’s performances are also presented.

On the Number of Containments in P-free Families

A subfamily {F_1,F_2,dots ,F_{|P|}}subseteq {{mathcal {F}}} is a copy of the poset P if there exists a bijection i:Prightarrow {F_1,F_2,dots ,F_{|P|}}, such that ple _P q implies i(p)subseteq i(q). A family {{mathcal {F}}} is P-free, if it does not contain a copy of P. In this paper we establish basic results on the maximum number of k-chains in a P-free family {{mathcal {F}}}subseteq 2^{[n]}. We prove that if the height of P, h(P) > k, then this number is of the order Theta (prod _{i=1}^{k+1}left( {begin{array}{c}l_{i-1} l_iend{array}}right) ), where l_0=n and l_1ge l_2ge dots ge l_{k+1} are such that n-l_1,l_1-l_2,dots , l_k-l_{k+1},l_{k+1} differ by at most one. On the other hand if h(P)le k, then we show that this number is of smaller order of magnitude. Let vee _r denote the poset on r+1 elements a, b_1, b_2, ldots , b_r, where a < b_i for all 1 le i le r and let wedge _r denote its dual. For any values of k and l, we construct a {wedge _k,vee _l}-free family and we conjecture that it contains asymptotically the maximum number of pairs in containment. We prove that this conjecture holds under the additional assumption that a chain of length 4 is forbidden. Moreover, we prove the conjecture for some small values of k and l. We also derive the asymptotics of the maximum number of copies of certain tree posets T of height 2 in {wedge _k,vee _l}-free families {{mathcal {F}}}subseteq 2^{[n]}.

Stability of Difference Scheme for a Semilinear Differential Algebraic System of Index (k, 0)

We consider a semilinear differential-algebraic system of partial differential equations of index (k, 0). We numerically solve this system by applying the spline-collocation method based on splitting the matrix pencil. The method has high accuracy coinciding with the smallest order of the approximating spline.

A note on entire functions sharing a finite set with their difference operators

In this note, we will show that an entire function is equal to its difference operator if it has a growth property and shares a set, where the set consists of two entire functions of smaller orders. This result generalizes a result of Li (Comput. Methods Funct. Theory 12:307–328, 2012 and partially answers Liu’s (J. Math. Anal. Appl. 359:384–393, 2009) question.