The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity $k$ $(kinmathbb{N})$ based on the generalized iterated Fourier series. The case of Fourier-Legendre series as well as the case of trigonotemric Fourier series are considered in details. The obtained expansion provides a possibility to represent the iterated Stratonovich stochastic integral in the form of iterated series of products of standard Gaussian random variables. Convergence in the mean of degree $2n$ $(nin mathbb{N})$ of the expansion is proved. Some modifications of the mentioned expansion were derived for the case $k=2$. One of them is based of multiple trigonomentric Fourier series converging almost everywhere in the square $[t, T]^2$. The results of the article can be applied to the numerical solution of Ito stochastic differential equations.

In cite{CC} the authors, investigating a model of population dynamics, find the following result. Let $Omegasubset mathbb{R}^N$, $Ngeq 1$, be a bounded smooth domain. The weighted eigenvalue problem $-Delta u =lambda m u $ in $Omega$ under homogeneous Dirichlet boundary conditions, where $lambda in mathbb{R}$ and $min L^infty(Omega)$, is considered. The authors prove the existence of minimizers $check m$ of the principal positive eigenvalue $lambda_1(m)$ when $m$ varies in a class $mathcal{M}$ of functions where average, maximum, and minimum values are given. A similar result is obtained in cite{CCP} when $m$ is in the class $mathcal{G}(m_0)$ of rearrangements of a fixed $m_0in L^infty(Omega)$. In our work we establish that, if $Omega$ is Steiner symmetric, then every minimizer in cite{CC,CCP} inherits the same kind of symmetry.

We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $mathcal{A}_{q,p}(widehat{gl}(N)_{c})$. We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space ($p, q, c$). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson brackets structures are then computed for which some universal features are described.

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 give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form $$ F(x,u,Du,D^2u) = 0 $$ under suitable structure conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply to weak solutions of an eigenvalue problem for the variable exponent $p$-Laplacian.

Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to $p$-Laplace double obstacle problems involving the Schr"odinger term: $-Delta_p u + mathbb{V}|u|^{p-2}u$ with bound constraints $psi_1 le u le psi_2$ in non-smooth domains. This problem has its own interest in mathematics, engineering, physics and other branches of science. Our approach makes a novel connection between the study of Calder'on-Zygmund theory for nonlinear Schr"odinger type equations and variational inequalities for double obstacle problems.

In this note, we establish a local maximum principle along Ricci flow under scaling invariant curvature condition. This unifies the known preservation of nonnegativity results along Ricci flow with unbounded curvature. By combining with the Dirichlet heat kernel estimates, we also give a more direct proof of Hochard's localized version of a maximum principle given by R. Bamler, E. Cabezas-Rivas, and B. Wilking on the lower bound of curvature conditions.

We investigate the Boundary Harnack Principle in H"older domains of exponent $alpha>0$ by the analytical method developed in our previous work "A short proof of Boundary Harnack Principle".

ErdH{o}s and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and R"odl asked whether there is some integer $qge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset has 3 triples with distinct colors, and $N$ is double exponential in $n$. We make the first nontrivial progress on this problem by providing a $q$-coloring with this property for all $qgeq 9$, where $N$ is exponential in $n^{2+cq}$ and $c>0$ is an absolute constant.

Embodiment is an important characteristic for all intelligent agents (creatures and robots), while existing scene description tasks mainly focus on analyzing images passively and the semantic understanding of the scenario is separated from the interaction between the agent and the environment. In this work, we propose the Embodied Scene Description, which exploits the embodiment ability of the agent to find an optimal viewpoint in its environment for scene description tasks. A learning framework with the paradigms of imitation learning and reinforcement learning is established to teach the intelligent agent to generate corresponding sensorimotor activities. The proposed framework is tested on both the AI2Thor dataset and a real world robotic platform demonstrating the effectiveness and extendability of the developed method.

We address the problem of handling provenance information in ELHr ontologies. We consider a setting recently introduced for ontology-based data access, based on semirings and extending classical data provenance, in which ontology axioms are annotated with provenance tokens. A consequence inherits the provenance of the axioms involved in deriving it, yielding a provenance polynomial as an annotation. We analyse the semantics for the ELHr case and show that the presence of conjunctions poses various difficulties for handling provenance, some of which are mitigated by assuming multiplicative idempotency of the semiring. Under this assumption, we study three problems: ontology completion with provenance, computing the set of relevant axioms for a consequence, and query answering.

For Convolutional Neural Network-based object detection, there is a typical dilemma: the spatial information is well kept in the shallow layers which unfortunately do not have enough semantic information, while the deep layers have a high semantic concept but lost a lot of spatial information, resulting in serious information imbalance. To acquire enough semantic information for shallow layers, Feature Pyramid Networks (FPN) is used to build a top-down propagated path. In this paper, except for top-down combining of information for shallow layers, we propose a novel network called Image Pyramid Guidance Network (IPG-Net) to make sure both the spatial information and semantic information are abundant for each layer. Our IPG-Net has two main parts: the image pyramid guidance transformation module and the image pyramid guidance fusion module. Our main idea is to introduce the image pyramid guidance into the backbone stream to solve the information imbalance problem, which alleviates the vanishment of the small object features. This IPG transformation module promises even in the deepest stage of the backbone, there is enough spatial information for bounding box regression and classification. Furthermore, we designed an effective fusion module to fuse the features from the image pyramid and features from the backbone stream. We have tried to apply this novel network to both one-stage and two-stage detection models, state of the art results are obtained on the most popular benchmark data sets, i.e. MS COCO and Pascal VOC.

We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $mathcal{NP}$-complete in the case where each side of the bipartitioning must contain a linear fraction of the nonzeros.

We present an improved exact branch-and-bound algorithm which finds the minimum communication volume for a given matrix and maximum allowed imbalance. The algorithm is based on a maximum-flow bound and a packing bound, which extend previous matching and packing bounds.

We implemented the algorithm in a new program called MP (Matrix Partitioner), which solved 839 matrices from the SuiteSparse collection to optimality, each within 24 hours of CPU-time. Furthermore, MP solved the difficult problem of the matrix cage6 in about 3 days. The new program is on average more than ten times faster than the previous program MondriaanOpt.

Benchmark results using the set of 839 optimally solved matrices show that combining the medium-grain/iterative refinement methods of the Mondriaan package with the hypergraph bipartitioner of the PaToH package produces sparse matrix bipartitionings on average within 10% of the optimal solution.

Participatory Design's vision of democratic participation assumes participants' feelings of agency in envisioning a collective future. But this assumption may be leaky when dealing with vulnerable populations. We reflect on the results of a series of activities aimed at supporting agentic-future-envisionment with a group of sex-trafficking survivors in Nepal. We observed a growing sense among the survivors that they could play a role in bringing about change in their families. They also became aware of how they could interact with available institutional resources. Reflecting on the observations, we argue that building participant agency on the small and personal interactions is necessary before demanding larger Political participation. In particular, a value of PD, especially for vulnerable populations, can lie in the process itself if it helps participants position themselves as actors in the larger world.

We present a new mouse cursor designed to facilitate the use of the mouse by people with peripheral vision loss. The pointer consists of a collection of converging straight lines covering the whole screen and following the position of the mouse cursor. We measured its positive effects with a group of participants with peripheral vision loss of different kinds and we found that it can reduce by a factor of 7 the time required to complete a targeting task using the mouse. Using eye tracking, we show that this system makes it possible to initiate the movement towards the target without having to precisely locate the mouse pointer. Using Fitts' Law, we compare these performances with those of full visual field users in order to understand the relation between the accuracy of the estimated mouse cursor position and the index of performance obtained with our tool.

Digital watermarking is a remarkable issue in the field of information security to avoid the misuse of images in multimedia networks. Although access to unauthorized persons can be prevented through cryptography, it cannot be simultaneously used for copyright protection or content authentication with the preservation of image integrity. Hence, this paper presents an optimized multipurpose blind watermarking in Shearlet domain with the help of smart algorithms including MLP and NSGA-II. In this method, four copies of the robust copyright logo are embedded in the approximate coefficients of Shearlet by using an effective quantization technique. Furthermore, an embedded random sequence as a semi-fragile authentication mark is effectively extracted from details by the neural network. Due to performing an effective optimization algorithm for selecting optimum embedding thresholds, and also distinguishing the texture of blocks, the imperceptibility and robustness have been preserved. The experimental results reveal the superiority of the scheme with regard to the quality of watermarked images and robustness against hybrid attacks over other state-of-the-art schemes. The average PSNR and SSIM of the dual watermarked images are 38 dB and 0.95, respectively; Besides, it can effectively extract the copyright logo and locates forgery regions under severe attacks with satisfactory accuracy.

Simplified Chinese to Traditional Chinese character conversion is a common preprocessing step in Chinese NLP. Despite this, current approaches have poor performance because they do not take into account that a simplified Chinese character can correspond to multiple traditional characters. Here, we propose a model that can disambiguate between mappings and convert between the two scripts. The model is based on subword segmentation, two language models, as well as a method for mapping between subword sequences. We further construct benchmark datasets for topic classification and script conversion. Our proposed method outperforms previous Chinese Character conversion approaches by 6 points in accuracy. These results are further confirmed in a downstream application, where 2kenize is used to convert pretraining dataset for topic classification. An error analysis reveals that our method's particular strengths are in dealing with code-mixing and named entities.

We utilize recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to analyze Gaussian random coding for massive multiple-access at finite message length. Soft iterative interference cancellation is found to closely approach the performance bounds recently found in [1]. The existence of two fundamentally different regimes in the trade-off between power and bandwidth efficiency reported in [2] is related to much older results in [3] on power optimization by linear programming. Furthermore, we tighten the achievability bounds of [1] in the low power regime and show that orthogonal constellations are very close to the theoretical limits for message lengths around 100 and above.

We propose Cotatron, a transcription-guided speech encoder for speaker-independent linguistic representation. Cotatron is based on the multispeaker TTS architecture and can be trained with conventional TTS datasets. We train a voice conversion system to reconstruct speech with Cotatron features, which is similar to the previous methods based on Phonetic Posteriorgram (PPG). By training and evaluating our system with 108 speakers from the VCTK dataset, we outperform the previous method in terms of both naturalness and speaker similarity. Our system can also convert speech from speakers that are unseen during training, and utilize ASR to automate the transcription with minimal reduction of the performance. Audio samples are available at https://mindslab-ai.github.io/cotatron, and the code with a pre-trained model will be made available soon.

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Sigma$ and a stochastic memoryless map $Psi$. After that, we extend the result to the class of large scale systems in which: $Sigma$ consists of many sub-systems; and $Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.

In this work, we consider a group of robots working together to manipulate a rigid object to track a desired trajectory in $SE(3)$. The robots have no explicit communication network among them, and they do no know the mass or friction properties of the object, or where they are attached to the object. However, we assume they share data from a common IMU placed arbitrarily on the object. To solve this problem, we propose a decentralized adaptive control scheme wherein each agent maintains and adapts its own estimate of the object parameters in order to track a reference trajectory. We present an analysis of the controller's behavior, and show that all closed-loop signals remain bounded, and that the system trajectory will almost always (except for initial conditions on a set of measure zero) converge to the desired trajectory. We study the proposed controller's performance using numerical simulations of a manipulation task in 3D, and with hardware experiments which demonstrate our algorithm on a planar manipulation task. These studies, taken together, demonstrate the effectiveness of the proposed controller even in the presence of numerous unmodelled effects, such as discretization errors and complex frictional interactions.

In this paper, we analyze the symbol error rate (SER) performance of the simultaneous wireless information and power transfer (SWIPT) enabled three-node differential decode-and-forward (DDF) relay networks, which adopt the power splitting (PS) protocol at the relay. The use of non-coherent differential modulation eliminates the need for sending training symbols to estimate the instantaneous channel state informations (CSIs) at all network nodes, and therefore improves the power efficiency, as compared with the coherent modulation. However, performance analysis results are not yet available for the state-of-the-art detectors such as the approximate maximum-likelihood detector. Existing works rely on Monte-Carlo simulation to show that there exists an optimal PS ratio that minimizes the overall SER. In this work, we propose a near-optimal detector with linear complexity with respect to the modulation size. We derive an accurate approximate SER expression, based on which the optimal PS ratio can be accurately estimated without requiring any Monte-Carlo simulation.

Bilateral occipital nerve release surgery was the first, significant step to relieving Scurry's debilitating post-concussive headaches.

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 […]

The post Website Redesign Checklist + 7 Handy Website Redesign Tips appeared first on WebFX Blog.

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, […]

The post What is a Favicon? [+4 Tips for Creating an Impactful Favicon] appeared first on WebFX Blog.

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

The post 10 Helpful Tips for How to Make Your Website More Accessible appeared first on WebFX Blog.

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 […]

The post 5 Simple Tips for How to Update Content on Your Website appeared first on WebFX Blog.

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?” […]

The post How Fast Should My Website Be? [+7 Tips for Speeding Up Your Site] appeared first on WebFX Blog.

Welcome back! In the first part of this series, we looked at a very "low-level" way to interact with a relational database by sending it raw SQL strings and retrieving the results. We created a very simple Express application that we can use as an example and deployed it on Heroku with a Postgres database.

In this part, we're going to examine a few libraries which build on top of that foundation, adding layers of abstraction that let you read and manipulate database data in a more "JavaScript-like" way.

With all due respect to Greta Thunberg and Billie Eilish, nobody had a better 2019 than Baby Yoda. The real star of the Disney+ flagship Star Wars series The Mandalorian, the little green puppeteering/CGI marvel (aka "the Child") might be the most adorable creature ever created.…

Back in November, we wrote about local singer-songwriter Eliza Johnson's musical project Eliza Catastrophe and her new album You, which she released on pre-loaded MP3 players. One thing we weren't able to mention in our interview — for contractual reasons — is that she had only a couple months prior auditioned for American Idol, and her performance finally aired on the ABC reality competition show Sunday night.…

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.…

Before my car broke down, I didn't ride the bus.…

A process for reductive amination of aliphatic cyanoaldehydes to aliphatic diamines comprising (1) providing a mixture of 1,3-cyanocyclohexane carboxaldehyde and/or 1,4-cyanocyclohexane carboxaldehyde; (2) contacting said mixture with a metal carbonate based solid bed or a weak base anion exchange resin bed at a temperature from 15 to 40 ° C. for a period of at least 1 minute; (3) thereby treating said mixture, wherein said treated mixture has a pH in the range of 6 to 9; (4) feeding said treated mixture, hydrogen, and ammonia into a continuous reductive amination reactor system; (6) contacting said treated mixture, hydrogen, and ammonia with each other in the presence of one or more heterogeneous metal based catalyst systems at a temperature from 80 ° C. to 160 ° C. and a pressure from 700 to 3500 psig; (7) thereby producing one or more cycloaliphatic diamines is provided.

A process for conversion of aliphatic bicyclic amines to aliphatic diamines including contacting one or more bicyclic amines selected from the group consisting of 3-azabicyclo[3.3.1]nonane and azabicyclo[3.3.1]non-2-ene with ammonia and hydrogen, and alcohols in the presence of heterogeneous metal based catalyst systems, a metal selected from the group consisting of Co, Ni, Ru, Fe, Cu, Re, Pd, and their oxides at a temperature from 140° C. to 200° C. and a pressure from 1540 to 1735 psig for at least one hour reactor systems; forming a product mixture comprising aliphatic diamine(s), bicyclic amine(s), ammonia, hydrogen, and alcohol(s); removing said product mixture from the reactor system; removing at least some of the ammonia, hydrogen, water, alcohols, bicyclic amines from said product mixture; thereby separating the aliphatic diamines from said product mixture.

A system and method for providing more than two levels of classification distinction of a user state are provided. The first and second general states of a user are sensed. The first general state is classified as either a first state or a second state, and the second general state is classified as either a third state or a fourth state. The user state of the user is then classified as one of at least three different classification states.

The present disclosure involves systems, software, and computer-implemented methods for providing process intelligence by correlating events from multiple business process systems to a single business scenario using configurable correlation strategies. An example method includes identifying a raw event associated with a sending business process and a receiving business process, identifying a sending business process attribute associated with the sending business process and a receiving business process attribute associated with the receiving business process, determining a correlation strategy for associating the raw event with a business scenario instance, the determination based at least in part on the sending business process attribute and the receiving business process attribute, and generating a visibility scenario event from the raw event according to the correlation strategy, the visibility scenario event associated with the business scenario instance.

Systems and methods are disclosed that may be implemented for network management system (NMS) configuration management support for network devices using a learning and natural language processing application to capture the usage and behavior of the Command Line Interface (CLI) of a network device with the aid of a CLI knowledge model, which in one example may be ontology-based.

A process for producing bio-oil from municipal solid waste, the process including: a) liquifying municipal solid waste, to obtain a mixture containing an oily phase containing bio-oil, a solid phase, and a first aqueous phase; b) treating the first aqueous phase from a) with an adsorbing material, to obtain a second aqueous phase; c) fermenting the second aqueous phase from b), to obtain a biomass; d) subjecting the biomass obtained in c) to the liquification a). The bio-oil obtained is advantageously used in the production of biofuels for motor vehicles or for the generation of electric energy or heat.

A method for producing a high viscosity, low volatiles blown stripped oil blend is provided. The method may include the steps of: (i) obtaining an oil blend of corn stillage oil and soybean oil having a weight ratio of corn stillage oil to soybean oil of from about 1:2 to 3:1; (ii) heating the oil blend to at least 90° C.; (iii) passing air through the heated oil blend to produce a blown oil having a viscosity of at least 50 cSt at 40° C.; and (iv) stripping the blown oil from step (iii) to reduce an acid value of the blown oil to less than 5.0 mg KOH/gram.

The present invention provides a use of a lipid composition for the preparation of a nutritional, pharmaceutical or nutraceutical composition or a functional food, for the prevention and treatment of gastrointestinal diseases and disorders, and for promoting intestinal development, maturation, adaptation and differentiation.

Described herein are nitrated lipids and methods of making and using the nitrated lipids.

The present invention relates to a cationic lipid having one or more biodegradable groups located in the mid- or distal section of a lipidic moiety (e.g., a hydrophobic chain) of the cationic lipid. These cationic lipids may be incorporated into a lipid particle for delivering an active agent, such as a nucleic acid. The invention also relates to lipid particles comprising a neutral lipid, a lipid capable of reducing aggregation, a cationic lipid of the present invention, and optionally, a sterol. The lipid particle may further include a therapeutic agent such as a nucleic acid.

A method for lowering content of a sterol in a highly unsaturated fatty acid-concentrated oil in a method to concentrate a highly unsaturated fatty acid by using a lipase reaction, may include removing the free form of the sterol from a raw material oil that includes a highly unsaturated fatty acid-containing glyceride prior to performing the lipase reaction; and thereafter concentrating the highly unsaturated fatty acid in the glyceride by using a lipase that is less reactive for the highly unsaturated fatty acid.

Disclosed are oil-extended olefin block copolymer compositions with precipitated silica. The precipitated silica reduces oil-bleed while maintaining composition softness.

Non water-soluble polymers with a comb structure and a (meth)acrylic skeleton on which are grafted side chains containing at least one hydrophobic monomer of the styrene or (meth)acrylic ester type on C1 to C4, and at least one hydroxy or methoxy polylakylene glycol monomer. The levels of monomers are such that the polymer is amphiphilic because it is both rich in hydrophobic monomer and polylakylene glycol monomer. These products, used in paper coating dispersions, enable an increase in their Brookfield™ viscosity, a reduction in their ACAV viscosity, and an improvement in their water retention, which makes them particularly well suited for dry extract and/or high deposit speed coatings.

Compounds of formula (I) ##STR1## in which R1 is hydrogen, O°, CN, NO, cyanomethyl, C1 -C12 -alkyl, C3 -C12 -alkenyl or C3 -C12 -alkynyl subject to the proviso that the carbon atom attached to the nitrogen atom is a primary carbon atom, C7 -C12 -aralkyl, C1 -C12 -acyl, 2,3-epoxypropyl, OH-monosubstituted C2 -C6 -alkyl or 2,3-dihydroxypropyl, R2 is hydrogen, C1 -C18 -alkyl, C5 -C18 -cycloalkyl, C6 -C18 -aryl or C7 -C18 -aryalkyl, R3 is C6 -C18 -aryl or a group of the formula (II) ##STR2## in which R1 is as defined above, n is an integer from 1 to 4 and R4 is an organic or inorganic radical of a valency equal to n are useful for stabilizing organic material against oxidative, thermal and/or light induced degradation.

The present invention relates to novel heterocycle-substituted diphosphonic acids, and the pharmaceutically-acceptable salts and esters thereof, in which the diphosphonate-substituted carbon atom moiety is attached to a carbon atom in a nitrogen-containing six membered ring heterocycle, preferably a piperidine ring. The heterocycle-substituted diphosphonic acid compounds have the general structure: ##STR1## wherein Z is a nitrogen-containing six membered ring heterocycle moiety selected from piperidinyl, diazinyl and triazinyl; m, n and m+n are from 0 to 10; Q is a covalent bond or a moiety selected from oxygen, sulfur or nitrogen; and R1, R2, R3 and R4 are substituent groups.The present invention further relates to pharmaceutical compositions containing these novel compounds. Finally this invention relates to methods for treating or preventing diseases characterized by abnormal calcium and phosphate metabolism by utilizing a compound or pharmaceutical composition of the present invention.

A diphosphite is provided derived from phosphorous trihalide, tetra alkyl hindered bisphenol, and a neoalkyl diol. The phosphites exhibit improved stability and are useful as thermal oxidative stabilizers for thermoplastic compositions.