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Keywords = small gaps between primes

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13 pages, 381 KB  
Article
Optimizing Test Pattern Compaction with Boolean Satisfiability Attack
by Yadi Zhong
Chips 2025, 4(4), 51; https://doi.org/10.3390/chips4040051 - 6 Dec 2025
Viewed by 285
Abstract
Test time per chip plays an essential role in manufacturing tests. Keeping a low number of test patterns becomes one of the prime objectives in concurrence with achieving the desired fault coverage. Unfortunately, finding an optimum set is an NP-hard problem. Today’s commercial [...] Read more.
Test time per chip plays an essential role in manufacturing tests. Keeping a low number of test patterns becomes one of the prime objectives in concurrence with achieving the desired fault coverage. Unfortunately, finding an optimum set is an NP-hard problem. Today’s commercial ATPG tools have significantly reduced the number of test patterns to achieve a high fault coverage. However, there is still a huge gap for reducing the total pattern count, equivalent to minimizing test costs in the production phase. In this paper, we propose two novel methods to lower the test pattern count to detect all stuck-at faults in a circuit with the same or higher fault coverage as in the commercial ATPG tool, e.g., TetraMAX II. The first approach begins by applying a small set of random patterns to solve easy-to-detect faults. The remaining faults are detected by the SAT-based attack on logic locking with converting all the remaining faults into one locked circuit. Each stuck-at fault is modeled with its equivalent key gate. The second approach selects the first few patterns generated by the ATPG tool and applies the SAT attack of logic locking to determine the test patterns for detecting the undetected faults. By exploiting the overall linear iteration complexity and the exponential removal of incorrect key combinations per each SAT attack iteration, it is feasible to significantly reduce the total pattern count while maintaining the same or higher fault coverage as the ATPG counterpart. We demonstrate the effectiveness of both approaches and show that we are able to achieve a more compact test pattern set compared to a commercial ATPG tool. Full article
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58 pages, 548 KB  
Article
Recent Results on Large Gaps Between Primes
by Michael Th. Rassias
Axioms 2025, 14(3), 198; https://doi.org/10.3390/axioms14030198 - 6 Mar 2025
Viewed by 1633
Abstract
One of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin and Tao. It was later improved in the joint paper of these four authors [...] Read more.
One of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin and Tao. It was later improved in the joint paper of these four authors with Maynard. One of the main ingredients of these results is old methods from Erdős and Rankin. Other ingredients are important breakthrough results from Goldston, Pintz and Yildirim, and their extension by Maynard on small gaps between primes. All these previous results are discussed in brief. The results on the appearance of k-th powers of primes contained in those large gaps obtained by the author in joint work with Maier are based on a combination of the results just described with the matrix method of Maier. Full article
(This article belongs to the Section Algebra and Number Theory)
30 pages, 5872 KB  
Article
New Solids in As-O-Mo, As(P)-O-Mo(W) and As(P)-O-Nb(W) Systems That Exhibit Nonlinear Optical Properties
by Nikolay Gerasimchuk, Lauri Kivijarvi, Bruce Noll, Meriem Goudjil, Soma Khanra, Yu Ping, Miles Pearson and Frank Röminger
Molecules 2021, 26(5), 1494; https://doi.org/10.3390/molecules26051494 - 9 Mar 2021
Viewed by 3290
Abstract
Interactions between well-mixed fine powders of As2O3, P2O5, MoO3, WO3 and Nb2O5 at different stoichiometry in quartz ampoules under vacuum at ~1000 °C in the presence of metallic molybdenum [...] Read more.
Interactions between well-mixed fine powders of As2O3, P2O5, MoO3, WO3 and Nb2O5 at different stoichiometry in quartz ampoules under vacuum at ~1000 °C in the presence of metallic molybdenum (or niobium), over several weeks, led to shiny dichroic crystalline materials being formed in cooler parts of the reaction vessel. An addition of small quantities of metals-Mo or Nb-was made with the aim of partially reducing their highly oxidized Mo(VI), W(VI) or Nb(V) species to corresponding Mo(V), W(V) and Nb(IV) centers, in order to form mixed valence solids. Sublimed crystals of four new compounds were investigated using a variety of techniques, with prime emphasis on the X-ray analysis, followed by spectroscopy (diffusion reflectance, IR, Raman and EPR), second harmonic generation (SHG), thermal analysis under N2 and air atmosphere, and single crystals electrical conductivity studies. The results evidenced the formation of new complex solids of previously unknown compositions and structures. Three out of four compounds crystallized in non-centrosymmetric space groups and represent layered 2D polymeric puckered structures that being stacked on each other form 3D lattices. All new solids exhibit strong second-harmonic-generation (SHG effect; based on YAG 1064 nm tests with detection of 532 nm photons), and a rare photosalient effect when crystals physically move in the laser beam. Single crystals’ electrical conductivity of the four new synthesized compounds was measured, and the results showed their semiconductor behavior. Values of band gaps of these new solids were determined using diffusion reflectance spectroscopy in the visible region. Aspects of new solids’ practical usefulness are discussed. Full article
(This article belongs to the Special Issue Recent Advances in Modern Inorganic Chemistry)
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14 pages, 1894 KB  
Review
Synaptic Vesicles Having Large Contact Areas with the Presynaptic Membrane are Preferentially Hemifused at Active Zones of Frog Neuromuscular Junctions Fixed during Synaptic Activity
by Jae Hoon Jung
Int. J. Mol. Sci. 2019, 20(11), 2692; https://doi.org/10.3390/ijms20112692 - 31 May 2019
Cited by 6 | Viewed by 5218
Abstract
Synaptic vesicles dock on the presynaptic plasma membrane of axon terminals and become ready to fuse with the presynaptic membrane or primed. Fusion of the vesicle membrane and presynaptic membrane results in the formation of a pore between the membranes, through which the [...] Read more.
Synaptic vesicles dock on the presynaptic plasma membrane of axon terminals and become ready to fuse with the presynaptic membrane or primed. Fusion of the vesicle membrane and presynaptic membrane results in the formation of a pore between the membranes, through which the vesicle’s neurotransmitter is released into the synaptic cleft. A recent electron tomography study on frog neuromuscular junctions fixed at rest showed that there is no discernible gap between or merging of the membrane of docked synaptic vesicles with the presynaptic membrane, however, the extent of the contact area between the membrane of docked synaptic vesicles and the presynaptic membrane varies 10-fold with a normal distribution. The study also showed that when the neuromuscular junctions are fixed during repetitive electrical nerve stimulation, the portion of large contact areas in the distribution is reduced compared to the portion of small contact areas, suggesting that docked synaptic vesicles with the largest contact areas are greatly primed to fuse with the membrane. Furthermore, the finding of several hemifused synaptic vesicles among the docked vesicles was briefly reported. Here, the spatial relationship of 81 synaptic vesicles with the presynaptic membrane at active zones of the neuromuscular junctions fixed during stimulation is described in detail. For the most of the vesicles, the combined thickness of each of their contact sites was not different from the sum of the membrane thicknesses of the vesicle membrane and presynaptic membrane, similar to the docked vesicles at active zones of the resting neuromuscular junctions. However, the combined membrane thickness of a small portion of the vesicles was considerably less than the sum of the membrane thicknesses, indicating that the membranes at their contact sites were fixed in a state of hemifusion. Moreover, the hemifused vesicles were found to have large contact areas with the presynaptic membrane. These findings support the recently proposed hypothesis that, at frog neuromuscular junctions, docked synaptic vesicles with the largest contact areas are most primed for fusion with the presynaptic membrane, and that hemifusion is a fusion intermediate step of the vesicle membrane with the presynaptic membrane for synaptic transmission. Full article
(This article belongs to the Special Issue Neurotransmitter Secretion and Release)
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14 pages, 1857 KB  
Article
Histopathology of the Liver, Kidney, and Spleen of Mice Exposed to Gold Nanoparticles
by Khalid Elfaki Ibrahim, Mohsen Ghaleb Al-Mutary, Amel Omer Bakhiet and Haseeb Ahmad Khan
Molecules 2018, 23(8), 1848; https://doi.org/10.3390/molecules23081848 - 25 Jul 2018
Cited by 178 | Viewed by 20119
Abstract
Gold nanoparticles (GNPs) are biocompatible nanomaterials that are currently researched for biomedical applications such as imaging and targeted drug delivery. In this investigation, we studied the effects of a single dose (injected on day 1) as well as a priming dose (two injections [...] Read more.
Gold nanoparticles (GNPs) are biocompatible nanomaterials that are currently researched for biomedical applications such as imaging and targeted drug delivery. In this investigation, we studied the effects of a single dose (injected on day 1) as well as a priming dose (two injections with a gap of one week) of 5 nm, 20 nm, and 50 nm diameter GNPs on the structural and biochemical changes in the liver, kidney, and spleen of mice. The results showed that small sized GNPs (5 nm) produced significant pathological changes in the liver on day 2 that gradually reduced on day 8. The medium (20 nm) and large (50 nm) sized GNPs preferentially targeted the spleen and caused significant pathological changes to the spleen architecture on day 2 that persisted on day 8 as well. There were minimal and insignificant pathological changes to the kidneys irrespective of the GNPs size. The animals that were primed with the pre-exposure of GNPs did not show any aggravation of histological changes after the second dose of the same GNPs. None of the dose regimens of the GNPs were able to significantly affect the markers of oxidative stress including glutathione (GSH) and malondialdehyde (MDA) in all of the organs that were studied. In conclusion, the size of GNPs plays an important role in their pathological effects on different organs of mice. Moreover, the primed animals become refractory to further pathological changes after the second dose of GNPs, suggesting the importance of a priming dose in medical applications of GNPs. Full article
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