Motivated by quotient algorithms, such as the well-known $p$-quotient or solvable quotient algorithms, we describe how to compute extensions $ ilde H$ of a finite group $H$ by a direct sum of isomorphic simple $mathbb{Z}_p H$-modules such that $H$ and $ ilde H$ have the same number of generators. Similar to other quotient algorithms, our description will be via a suitable covering group of $H$. Defining this covering group requires a study of the representation module, as introduced by Gasch"utz in 1954. Our investigation involves so-called Fox derivatives (coming from free differential calculus) and, as a by-product, we prove that these can be naturally described via a wreath product construction. An important application of our results is that they can be used to compute, for a given epimorphism $G o H$ and simple $mathbb{Z}_p H$-module $V$, the largest quotient of $G$ that maps onto $H$ with kernel isomorphic to a direct sum of copies of $V$. For this we also provide a description of how to compute second cohomology groups for the (not necessarily solvable) group $H$, assuming a confluent rewriting system for $H$. To represent the corresponding group extensions on the computer, we introduce a new hybrid format that combines this rewriting system with the polycyclic presentation of the module.

Let $hat G$ be the finite simply connected version of an exceptional Chevalley group, and let $V$ be a nontrivial irreducible module, of minimal dimension, for $hat G$ over its field of definition. We explore the overgroup structure of $hat G$ in $mathrm{GL}(V)$, and the submodule structure of the exterior square (and sometimes the third Lie power) of $V$. When $hat G$ is defined over a field of odd prime order $p$, this allows us to construct the smallest (with respect to certain properties) $p$-groups $P$ such that the group induced by $mathrm{Aut}(P)$ on $P/Phi(P)$ is either $hat G$ or its normaliser in $mathrm{GL}(V)$.

Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)in G^{(k)}$ such that $w(g_1,...,g_k)=1$. Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit's conjecture, and prove that $N_w(g) ge |G|^{k-2}$, where $g$ is a $w$-value in $G$, for finite groups $G$ of odd order and nilpotency class 2. If $w$ is a word in two variables, we further show that $N_w(g) ge |G|$, where $g$ is a $w$-value in $G$ for finite groups $G$ of nilpotency class 2. In addition, for $p$ a prime, we show that finite $p$-groups $G$, with two distinct irreducible complex character degrees, satisfy the generalized Amit conjecture for words $w_k =[x_1,y_1]...[x_k,y_k]$ with $k$ a natural number; that is, for $g$ a $w_k$-value in $G$ we have $N_{w_k}(g) ge |G|^{2k-1}$.

Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.

In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.

Let the group $G = AB$ be the product of subgroups $A$ and $B$, and let $p$ be a prime. We prove that $p$ does not divide the conjugacy class size (index) of each $p$-regular element of prime power order $xin Acup B$ if and only if $G$ is $p$-decomposable, i.e. $G=O_p(G) imes O_{p'}(G)$.

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to c-groups and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.

Given an one-dimensional Lorenz-like expanding map we prove that the conditionlinebreak $P_{top}(phi,partial mathcal{P},ell)<P_{top}(phi,ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials $phi:[0,1]longrightarrow mathbb{R}$. We apply this to prove that quasi-H"older-continuous potentials (see, subsection 2.2 for definition) have at most one equilibrium measure and we construct a family of continuous but not H"older and neither weak H"older continuous potentials for which we observe phase transitions. Indeed, this class includes all H"older and weak-H"older continuous potentials and form an open and [2].

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.

In this paper we study removable singularities for regular $(1,1/2)$-Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric capacity and we study its metric and geometric properties and the connection with the $L^2$ boundedness of the singular integral whose kernel is given by the gradient of the fundamental solution of the heat equation.

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $mathrm{GL}_n(E)$. Let $pi$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $iota_P^G pi$ is reducible.

We construct a smooth moduli stack of tuples consisting of genus two nodal curves, line bundles, and twisted fields. It leads to a desingularization of the moduli of genus two stable maps to projective spaces. The construction of this new moduli is based on systematical application of the theory of stacks with twisted fields (STF), which has its prototype appeared in arXiv:1906.10527 and arXiv:1201.2427 and is fully developed in this article. The results of this article are the second step of a series of works toward the resolutions of the moduli of stable maps of higher genera.

Let $E$ be the self-similar set generated by the {it iterated function system} {[ f_0(x)=frac{x}{eta},quad f_1(x)=frac{x+1}{eta}, quad f_{eta+1}=frac{x+eta+1}{eta} ]}with $etage 3$. {Then} $E$ is a self-similar set with complete {overlaps}, i.e., $f_{0}circ f_{eta+1}=f_{1}circ f_1$, but $E$ is not totally self-similar.

We investigate all its generating iterated function systems, give the spectrum of $E$, and determine the Hausdorff dimension and Hausdorff measure of $E$ and of the sets which contain all points in $E$ having finite or infinite different triadic codings.

The congruence subgroup problem for a finitely generated group $Gamma$ and $Gleq Aut(Gamma)$ asks whether the map $hat{G} o Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(G,Gamma ight)$? Here $hat{X}$ denotes the profinite completion of $X$. In the case $G=Aut(Gamma)$ we denote $Cleft(Gamma ight)=Cleft(Aut(Gamma),Gamma ight)$.

Let $Gamma$ be a finitely generated group, $ar{Gamma}=Gamma/[Gamma,Gamma]$, and $Gamma^{*}=ar{Gamma}/tor(ar{Gamma})congmathbb{Z}^{(d)}$. Denote $Aut^{*}(Gamma)= extrm{Im}(Aut(Gamma) o Aut(Gamma^{*}))leq GL_{d}(mathbb{Z})$. In this paper we show that when $Gamma$ is nilpotent, there is a canonical isomorphism $Cleft(Gamma ight)simeq C(Aut^{*}(Gamma),Gamma^{*})$. In other words, $Cleft(Gamma ight)$ is completely determined by the solution to the classical congruence subgroup problem for the arithmetic group $Aut^{*}(Gamma)$.

In particular, in the case where $Gamma=Psi_{n,c}$ is a finitely generated free nilpotent group of class $c$ on $n$ elements, we get that $C(Psi_{n,c})=C(mathbb{Z}^{(n)})={e}$ whenever $ngeq3$, and $C(Psi_{2,c})=C(mathbb{Z}^{(2)})=hat{F}_{omega}$ = the free profinite group on countable number of generators.

In this paper, we give new constructions of strongly regular Cayley graphs on abelian groups as generalizations of a series of known constructions: the construction of covering extended building sets in finite fields by Xia (1992), the product construction of Menon-Hadamard difference sets by Turyn (1984), and the construction of Paley type partial difference sets by Polhill (2010). Then, we obtain new large families of strongly regular Cayley graphs of Latin square type or negative Latin square type.

In response to the coronavirus disease (COVID-19) outbreak, there is an ever-increasing number of national governments that are rolling out contact-tracing Apps to aid the containment of the virus. The first hugely contentious issue facing the Apps is the deployment framework, i.e. centralised or decentralised. Based on this, the debate branches out to the corresponding technologies that underpin these architectures, i.e. GPS, QR codes, and Bluetooth. This work conducts a pioneering review of the above scenarios and contributes a geolocation mapping of the current deployment. The vulnerabilities and the directions of research are identified, with a special focus on the Bluetooth-based decentralised scheme.

We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each query and the other determining the *column*.

We construct PCPs that are efficient, short, smooth and (almost-)rectangular. As a key application, we show that proofs for hard languages in NTIME$(2^n)$, when viewed as matrices, are rigid infinitely often. This strengthens and considerably simplifies a recent result of Alman and Chen [FOCS, 2019] constructing explicit rigid matrices in FNP. Namely, we prove the following theorem: - There is a constant $delta in (0,1)$ such that there is an FNP-machine that, for infinitely many $N$, on input $1^N$ outputs $N imes N$ matrices with entries in $mathbb{F}_2$ that are $delta N^2$-far (in Hamming distance) from matrices of rank at most $2^{log N/Omega(log log N)}$.

Our construction of rectangular PCPs starts with an analysis of how randomness yields queries in the Reed--Muller-based outer PCP of Ben-Sasson, Goldreich, Harsha, Sudan and Vadhan [SICOMP, 2006; CCC, 2005]. We then show how to preserve rectangularity under PCP composition and a smoothness-inducing transformation. This warrants refined and stronger notions of rectangularity, which we prove for the outer PCP and its transforms.

Unsupervised machine translation (MT) has recently achieved impressive results with monolingual corpora only. However, it is still challenging to associate source-target sentences in the latent space. As people speak different languages biologically share similar visual systems, the potential of achieving better alignment through visual content is promising yet under-explored in unsupervised multimodal MT (MMT). In this paper, we investigate how to utilize visual content for disambiguation and promoting latent space alignment in unsupervised MMT. Our model employs multimodal back-translation and features pseudo visual pivoting in which we learn a shared multilingual visual-semantic embedding space and incorporate visually-pivoted captioning as additional weak supervision. The experimental results on the widely used Multi30K dataset show that the proposed model significantly improves over the state-of-the-art methods and generalizes well when the images are not available at the testing time.

With the growing reliance on the ubiquitous availability of IT systems and services, these systems become more global, scaled, and complex to operate. To maintain business viability, IT service providers must put in place reliable and cost efficient operations support. Artificial Intelligence for IT Operations (AIOps) is a promising technology for alleviating operational complexity of IT systems and services. AIOps platforms utilize big data, machine learning and other advanced analytics technologies to enhance IT operations with proactive actionable dynamic insight.

In this paper we share our experience applying the AIOps approach to a production cloud object storage service to get actionable insights into system's behavior and health. We describe a real-life production cloud scale service and its operational data, present the AIOps platform we have created, and show how it has helped us resolving operational pain points.

Does your website feature design straight out of the ’90s and functionality from the stone age? If so, it’s time for an upgrade — and WebFX can help. When it comes to website redesign checklists, we’re at the top of our game, and we know how to get things done. But where do you start […]

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When you bookmark pages on the web, it’s challenging to remember the name of the page. As you dive back into your bookmarks to find it, you see a small icon next to the page. You recognize the icon and realize it’s the website you viewed prior. This icon, known as a favicon, is small, […]

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In this article, we'll explore 10 quick and easy ways to improve your site's accessibility.

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WordPress powers 35% of all websites, which makes WordPress sites a go-to target for hackers. If you’re like most WordPress site owners, you’re probably asking the same question: Is my WordPress site secure? While you can’t guarantee site security, you can take several steps to improve and maximize your WordPress security. Keep reading to learn […]

The post Is My WordPress Site Secure? 13 Tips for Locking Down Your WordPress Site appeared first on WebFX Blog.

Subscribe to our YouTube channel for the latest in digital marketing! Transcript: Your website isn’t set in stone, so you shouldn’t treat it like it is.  Technology and the internet change quickly, and often. You should update your website regularly to keep up with the times. Having an up-to-date and optimized site creates a great […]

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Your website is your virtual business card and it often provides the first impression of your business to future customers — making it one of the most important aspects of your company. But if your website still has cobwebs from the 2000s, it’s time to put together a website redesign process. A website redesign process […]

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Perhaps no choice is as vital to marketing as color. Whether you are selecting the color for a product or for your email marketing campaign, color has a tremendous impact on all of us. Subconsciously, we associate different colors with different things. This infographic examines the psychology of color and looks at some common associations […]

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Did you know that for every second faster your website loads, you increase conversions by 7%? A fast loading website leads to longer dwell sessions, improved engagement, and increased conversions. When people can access information fast, they’re more likely to stay on your page. So now you’re probably wondering, “How fast should my website be?” […]

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The Cannabis Issue During normal times, I-90 Green House is like a destination resort for marijuana lovers.…

[IMAGE-1]After having their school year totally disrupted by the coronavirus pandemic, a return to some semblance of normalcy come summer is all many school-age kids and their families are looking forward to. For many, this anticipation includes annual summer camp traditions, from sleep-away adventures on the lake to fun-filled day camps for arts, learning or team sports.…

Summer Camps 2020 "Regional Summer Camps Hope the Pandemic Doesn't Put Activities on Pause, But Have Backup Plans Ready if it Does" …

At these gatherings in northeast Washington, the jackboot of tyranny is always said to be descending, the hand of the federal government always inches away from stealing your guns, your land, your freedom to speak or to pray.…

The CDC designed a flawed test for COVID-19, then took weeks to figure out a fix so state and local labs could use it. New York still doesn’t trust the test’s accuracy By Caroline Chen, Marshall Allen, Lexi Churchill and Isaac Arnsdorf Propublica…

[IMAGE-1] First of all: No. Why would a suddenly single dad to traumatized young children leave said shocked and distressed kids with his new fiancée, who is also the sole survivor of her own massive childhood trauma?…

Calling all fearless freaks! Mark your calendars: The Flaming Lips have rescheduled their now-canceled April gig at the Fox Theater for March 19, 2021.…

A coalition of immigrant-focused organizations has created the Spokane Relief Fund for Undocumented Immigrants, in order to help families who are unable to access federal aid during the coronavirus shutdowns. The partners sponsoring the work include the Spokane Immigrant Rights Coalition (SIRC), the Hispanic Business and Professional Association, Latinos en Spokane, Mujeres in Action and Raiz.…

As this issue goes to press we are all staying home to battle the coronavirus.…

Growing up, Luke Parker played sports.…

It’s March. The regular season is now in the rearview mirror.…

An aqueous dispersion includes particles at least partially encapsulated in a microgel where the microgel is prepared from a hyperbranched acrylic polymer. In addition, a method for making an aqueous dispersion includes: (1) mixing in an aqueous medium: (a) particles, (b) at least one ethylenically unsaturated monomer, and (c) a water-dispersible hyperbranched acrylic polymer having ethylenic unsaturation; and (2) polymerizing the at least one ethylenically unsaturated monomer and water-dispersible hyperbranched acrylic polymer having ethylenic unsaturation to at least partially encapsulate the particles in a microgel.

Polysubstituted cyclopentadiene compound wherein at least two different substituents are present from the group consisting of linear, branched and cyclic alkyls, aralkyls and alkenyls, and a process for the preparation of a cyclopentadiene compound substituted with at least two different groups chosen from the group consisting of linear, branched, cyclic and aromatic alkyls and alkenyls, characterized in that it comprises the reacting of a halide of a first substituting group in a mixture of the cyclopentadiene compound and an aqueous solution of a base, in which the quantity of the base relative to the cyclopentadiene compound is between 5 and 30 mol/mol, in the presence of a phase transfer catalyst, followed by the addition of a halide of a second or optionally a third substituting group to the reaction mixture.

Embodiments are directed to glass frits containing phosphors that can be used in LED lighting devices and for methods associated therewith for making the phosphor containing glass frit and their use in glass articles, for example, LED devices.

Shape memory and pseudoelastic martensitic behavior is enabled by a structure in which there is provided a crystalline ceramic material that is capable of undergoing a reversible martensitic transformation and forming martensitic domains, during such martensitic transformation, that have an elongated domain length. The ceramic material is configured as a ceramic material structure including a structural feature that is smaller than the elongated domain length of the ceramic material.

A memory device includes a semiconductor channel, a tunnel dielectric layer located over the semiconductor channel, a first charge trap including a plurality of electrically conductive nanodots located over the tunnel dielectric layer, dielectric separation layer located over the nanodots, a second charge trap including a continuous metal layer located over the separation layer, a blocking dielectric located over the second charge trap, and a control gate located over the blocking dielectric.

Disclosed is an epoxy resin composition used for encapsulation of a semiconductor containing an epoxy resin (A), a curing agent (B), an inorganic filler (C) and a mold releasing agent, in which the mold releasing agent contains a compound (D) having a copolymer of an α-olefin having 28 to 60 carbon atoms and a maleic anhydride esterified with a long chain aliphatic alcohol having 10 to 25 carbon atoms.

The present disclosure relates to a method for detecting a parity error in a sequence of DQPSK symbols of a digital transmission system, comprising determining a first demodulated symbol r1; determining a second demodulated symbol r2; determining a first parity symbol p1; determining a second parity symbol p2; determining a super-parity symbol q1; and detecting a parity error in the sequence of DQPSK symbols by comparing a combination of the first parity symbol p1 and the second parity symbol p2 against the super-parity symbol q1, wherein a parity between two DQPSK symbols describes a phase difference between the two DQPSK symbols.

A circuit arrangement and method couple a hardware-based pseudorandom number generator (PRNG) to an execution unit in such a manner that pseudorandom numbers generated by the PRNG may be selectively output to the execution unit for use as an operand during the execution of instructions by the execution unit. A PRNG may be coupled to an input of an operand multiplexer that outputs to an operand input of an execution unit so that operands provided by instructions supplied to the execution unit are selectively overridden with pseudorandom numbers generated by the PRNG. Furthermore, overridden operands provided by instructions supplied to the execution unit may be used as seed values for the PRNG.

A method for generating multi-level (or multi-bit) pseudo-random sequences is disclosed. This embodiment relates to communication systems, and more particularly to generating multi-level pseudo random symbol sequence. Present day systems do not employ effective mechanisms for generation of multi level PRBS in order to increase the data communication rates. Further, these systems do not cover all the possible transitions for the outputs of the system. The proposed system employs mechanisms in order to generate PRBS signals for producing multi levels signals to the electronic components. The mechanism employs alternate bit tapping techniques. In the alternate bit tapping technique, bits are tapped alternatively to determine the current state and the next state of the system. In addition, the mechanism also covers all the possible states of the output vector with transitions between the output states. This ensures that high data rates are obtained for a given bandwidth of operation.

A usage allocation of a hardware resource to each of a number of workloads over time is determined using a demand model. The usage allocation of the resource includes a current and past actual usage allocation of the resource, a future projected usage allocation of the resource, and current and past actual usage of the resource. A capacity allocation of the resource is determined using a capacity model. The capacity allocation of the resource includes a current and past capacity and a future projected capacity of the resource. Whether a gap exists between the usage allocation and the capacity allocation is determined using a mapping model. Where the gap exists between the usage allocation of the resource and the capacity allocation of the resource, a user is presented with options determined using the mapping model and selectable by the user to implement a remediation strategy to close the gap.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

The present invention relates to a method for compiling code for a multi-core processor, comprising: detecting and optimizing a loop, partitioning the loop into partitions executable and mappable on physical hardware with optimal instruction level parallelism, optimizing the loop iterations and/or loop counter for ideal mapping on hardware, chaining the loop partitions generating a list representing the execution sequence of the partitions.