Enhancement of the Tracking Performance for Robot Manipulator by Using the Feed-forward Scheme and Reasonable Switching Mechanism

Robot manipulator has become an exciting topic for many researchers during several decades. They have investigated the advanced algorithms such as sliding mode control, neural network, or genetic scheme to implement these developments. However, they lacked the integration of these algorithms to explore many potential expansions. Simultaneously, the complicated system requires a lot of computational costs, which is not always supported. Therefore, this paper presents a novel design of switching mechanisms to control the robot manipulator. This investigation is expected to achieve superior performance by flexibly adjusting various strategies for better selection. The Proportional-Integral-Derivative (PID) scheme is well-known, easy to implement, and ensures rapid computation while it might not have much control effect. The advanced interval type-2 fuzzy sliding mode control properly deals with nonlinear factors and disturbances. Consequently, the PID scheme is switched when the tracking error is less than the threshold or is far from the target. Otherwise, the interval type-2 fuzzy sliding mode control scheme is activated to cope with unknown factors. The main contributions of this paper are (i) the recommendation of a suitable switching mechanism to drive the robot manipulator, (ii) the successful integration of the interval type-2 fuzzy sliding mode control to track the desired trajectory, and (iii) the launching of several tests to validate the proposed controller with robot model. From these achievements, it would be stated that the proposed approach is effective in tracking performance, robust in disturbance-rejection, and feasible in practical implementation

Decreasing behavior of the depth functions of edge ideals

Let $I$ be the edge ideal of a connected non-bipartite graph and $R$ the base polynomial ring. Then $\operatorname{depth} R/I \ge 1$ and $\operatorname{depth} R/I^t = 0$ for $t \gg 1$. We give combinatorial conditions for $\operatorname{depth} R/I^t = 1$ for some $t$ in between and show that the depth function is non-increasing thereafter. Especially, the depth function quickly decreases to 0 after reaching 1. We show that if $\operatorname{depth} R/I = 1$ then $\operatorname{depth} R/I^2 = 0$ and if $\operatorname{depth} R/I^2 = 1$ then $\operatorname{depth} R/I^5 = 0$. Other similar results suggest that if $\operatorname{depth} R/I^t = 1$ then $\operatorname{depth} R/I^{t+3} = 0$. This a surprising phenomenon because the depth of a power can determine a smaller depth of another power. Furthermore, we are able to give a simple combinatorial criterion for $\operatorname{depth} R/I^{(t)} = 1$ for $t \gg 1$ and show that the condition $\operatorname{depth} R/I^{(t)} = 1$ is persistent, where $I^{(t)}$ denotes the $t$-th symbolic powers of $I$.Comment: 15 pages, 3 figure

A general formula for the index of depth stability of edge ideals

By a classical result of Brodmann, the function $\operatorname{depth} R/I^t$ is asymptotically a constant, i.e. there is a number $s$ such that $\operatorname{depth} R/I^t = \operatorname{depth} R/I^s$ for $t > s$. One calls the smallest number $s$ with this property the index of depth stability of $I$ and denotes it by $\operatorname{dstab}(I)$. This invariant remains mysterious til now. The main result of this paper gives an explicit formula for $\operatorname{dstab}(I)$ when $I$ is an arbitrary ideal generated by squarefree monomials of degree 2. That is the first general case where one can characterize $\operatorname{dstab}(I)$ explicitly. The formula expresses $\operatorname{dstab}(I)$ in terms of the associated graph. The proof involves new techniques which relate different topics such as simplicial complexes, systems of linear inequalities, graph parallelizations, and ear decompositions. It provides an effective method for the study of powers of edge ideals.Comment: 23 pages, 4 figure

Lactic Acid Fermentation of Radish and Cucumber in Rice Bran Bed

The Lactobacillus plantarum (L. plantarum) strain XK1.4 isolated from pickled vegetables was applied for cucumber and radish fermentation using rice bran. Fermented radish and cucumber pickles are the lactic acid fermentation products formed through the influence of microorganisms present in the environment. The main objective of the study is to select the appropriate rice bran type (white/yellow rice bran) and treatment methods (roasting time), and also choose suitable fermentation conditions (initial microbial population and added salt content) for traditional pickled cucumber and white radish with appropriate lactic acid content and high acceptability by consumers. The results showed that the quality of white bran was better than yellow bran and less oxidized, the total free fatty acid was also much lower than that of yellow bran. It was found that the lactic acid content analyses provided significant different results for the samples, compared to the control (without inoculant addition). The pickled samples for which L. plantarum strain XK 1.4 was used displayed a better fermentation process. The lower concentration of bacteria added in the initial stage, the lower the acid content of the rice bran medium and the fermented products where L. plantarum strains were added. L. plantarum grew rapidly in rice bran fermenting bed of 10 CFU g at 25-26 °C and 3% NaCl. With the appropriate selection of fermentation parameters, it only takes about 4 days for the fermentation process (2 days of preparing rice bran medium and 2 days of fermenting white radish and cucumber) with high lactic acid content and consumer’s acceptability

Lactic Acid Fermentation of Radish and Cucumber in Rice Bran Bed

The Lactobacillus plantarum (L. plantarum) strain XK1.4 isolated from pickled vegetables was applied for cucumber and radish fermentation using rice bran. Fermented radish and cucumber pickles are the lactic acid fermentation products formed through the influence of microorganisms present in the environment. The main objective of the study is to select the appropriate rice bran type (white/yellow rice bran) and treatment methods (roasting time), and also choose suitable fermentation conditions (initial microbial population and added salt content) for traditional pickled cucumber and white radish with appropriate lactic acid content and high acceptability by consumers. The results showed that the quality of white bran was better than yellow bran and less oxidized, the total free fatty acid was also much lower than that of yellow bran. It was found that the lactic acid content analyses provided significant different results for the samples, compared to the control (without inoculant addition). The pickled samples for which L. plantarum strain XK 1.4 was used displayed a better fermentation process. The lower concentration of bacteria added in the initial stage, the lower the acid content of the rice bran medium and the fermented products where L. plantarum strains were added. L. plantarum grew rapidly in rice bran fermenting bed of 10 CFU g at 25-26 °C and 3% NaCl. With the appropriate selection of fermentation parameters, it only takes about 4 days for the fermentation process (2 days of preparing rice bran medium and 2 days of fermenting white radish and cucumber) with high lactic acid content and consumer’s acceptability

Equality of ordinary and symbolic powers of Stanley-Reisner ideals

This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main results are combinatorial characterizations of such complexes in the two-dimensional case. It turns out that there exist only a finite number of complexes with this property and that these complexes can be described completely. As a consequence we are able to determine all complexes for which the m-th ordinary power of the Stanley-Reisner ideal is Cohen-Macaulay for a given m > 1.Comment: 19 page