329 research outputs found

    Submerged Cultivation Of Morel Mushroom Mycelium In Waste Sulfite Liquors

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    Incidences between points and generalized spheres over finite fields and related problems

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    Let Fq\mathbb{F}_q be a finite field of qq elements where qq is a large odd prime power and Q=a1x1c1+...+adxdcdFq[x1,...,xd]Q =a_1 x_1^{c_1}+...+a_dx_d^{c_d}\in \mathbb{F}_q[x_1,...,x_d], where 2ciN2\le c_i\le N, gcd(ci,q)=1\gcd(c_i,q)=1, and aiFqa_i\in \mathbb{F}_q for all 1id1\le i\le d. A QQ-sphere is a set of the form {xFqdQ(xb)=r}\lbrace x\in \mathbb{F}_q^d | Q(x-b)=r\rbrace, where bFqd,rFqb\in \mathbb{F}_q^d, r\in \mathbb{F}_q. We prove bounds on the number of incidences between a point set P\mathcal{P} and a QQ-sphere set S\mathcal{S}, denoted by I(P,S)I(\mathcal{P},\mathcal{S}), as the following. I(P,S)PSqqd/2PS.| I(\mathcal{P},\mathcal{S})-\frac{|\mathcal{P}||\mathcal{S}|}{q}|\le q^{d/2}\sqrt{|\mathcal{P}||\mathcal{S}|}. We prove this estimate by studying the spectra of directed graphs. We also give a version of this estimate over finite rings Zq\mathbb{Z}_q where qq is an odd integer. As a consequence of the above bounds, we give an estimate for the pinned distance problem. In Sections 44 and 55, we prove a bound on the number of incidences between a random point set and a random QQ-sphere set in Fqd\mathbb{F}_q^d. We also study the finite field analogues of some combinatorial geometry problems, namely, the number of generalized isosceles triangles, and the existence of a large subset without repeated generalized distances.Comment: to appear in Forum Mat

    Development of Multi-Robotic Arm System for Sorting System Using Computer Vision

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    This paper develops a multi-robotic arm system and a stereo vision system to sort objects in the right position according to size and shape attributes. The robotic arm system consists of one master and three slave robots associated with three conveyor belts. Each robotic arm is controlled by a robot controller based on a microcontroller. A master controller is used for the vision system and communicating with slave robotic arms using the Modbus RTU protocol through an RS485 serial interface. The stereo vision system is built to determine the 3D coordinates of the object. Instead of rebuilding the entire disparity map, which is computationally expensive, the centroids of the objects in the two images are calculated to determine the depth value. After that, we can calculate the 3D coordinates of the object by using the formula of the pinhole camera model. Objects are picked up and placed on a conveyor branch according to their shape. The conveyor transports the object to the location of the slave robot. Based on the size attribute that the slave robot receives from the master, the object is picked and placed in the right position. Experiment results reveal the effectiveness of the system. The system can be used in industrial processes to reduce the required time and improve the performance of the production line

    A Critique of Chen's "The 2-MAXSAT Problem Can Be Solved in Polynomial Time"

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    In this paper, we examine Yangjun Chen's technical report titled ``The 2-MAXSAT Problem Can Be Solved in Polynomial Time'' [Che23], which revises and expands upon their conference paper of the same name [Che22]. Chen's paper purports to build a polynomial-time algorithm for the NP{\rm NP}-complete problem 2-MAXSAT by converting a 2-CNF formula into a graph that is then searched. We show through multiple counterexamples that Chen's proposed algorithms contain flaws, and we find that the structures they create lack properly formalized definitions. Furthermore, we elaborate on how the author fails to prove the correctness of their algorithms and how they make overgeneralizations in their time analysis of their proposed solution. Due to these issues, we conclude that Chen's technical report [Che23] and conference paper [Che22] both fail to provide a proof that P=NP{\rm P}={\rm NP}.Comment

    Optical Hall response of bilayer graphene: the manifestation of chiral hybridised states in broken mirror symmetry lattices

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    Understanding the mechanisms governing the optical activity of layered-stacked materials is crucial to the design of devices aimed at manipulating light at the nanoscale. Here, we show that both twisted and slid bilayer graphene are chiral systems that can deflect the polarization of linear polarized light. However, only twisted bilayer graphene supports circular dichroism. Our calculation scheme, which is based on the time-dependent Schr\"odinger equation, is particularly efficient for calculating the optical-conductivity tensor. Specifically, it allows us to show the chirality of hybridized states as the handedness-dependent bending of the trajectory of kicked Gaussian wave packets in bilayer lattices. We show that nonzero Hall conductivity is the result of the noncanceling manifestation of hybridized states in chiral lattices. We also demonstrate the continuous dependence of the conductivity tensor on the twist angle and the sliding vector.Comment: 24 pages, 6 figure
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