We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex homotopy equivalent to the exotic Springer fiber. This homotopy equivalent space admits an action of the type C Weyl group inducing Kato's original exotic Springer representation on cohomology. Our results are described in terms of the diagrammatics of the one-boundary Temperley-Lieb algebra (also known as the blob algebra). This provides a first step in generalizing the geometric versions of Khovanov's arc algebra to the exotic setting.

In this paper, we show that the difference between the number of parts in the odd partitions of $n$ and the number of parts in the distinct partitions of $n$ satisfies Euler's recurrence relation for the partition function $p(n)$ when $n$ is odd. A decomposition of this difference in terms of the total number of parts in all the partitions of $n$ is also derived. In this context, we conjecture that for $k>0$, the series

$$

(q^2;q^2)_infty sum_{n=k}^infty frac{q^{{kchoose 2}+(k+1)n}}{(q;q)_n}

egin{bmatrix}

n-1\k-1

end{bmatrix}

$$ has non-negative coefficients.

A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. (British J. of Math. & CS. 8 (2015), 330-336). Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with corresponding parameters. We also deal with the probability of each of the variables being the maximal one.

The calculations lead to expressions involving Hurwitz's zeta function at certain special points. We find here explicitly the values of the function at these points. Also, the distribution function of the maximum we deal with is closely related to the generating function of the partition function. Thus, our results (and proofs) rely on classical results pertaining to the partition function.

The problem of minimizing an entropy functional subject to linear constraints is a useful example of partially finite convex programming. In the 1990s, Borwein and Lewis provided broad and easy-to-verify conditions that guarantee strong duality for such problems. Their approach is to construct a function in the quasi-relative interior of the relevant infinite-dimensional set, which assures the existence of a point in the core of the relevant finite-dimensional set. We revisit this problem, and provide an alternative proof by directly appealing to the definition of the core, rather than by relying on any properties of the quasi-relative interior. Our approach admits a minor relaxation of the linear independence requirements in Borwein and Lewis' framework, which allows us to work with certain piecewise-defined moment functions precluded by their conditions. We provide such a computed example that illustrates how this relaxation may be used to tame observed Gibbs phenomenon when the underlying data is discontinuous. The relaxation illustrates the understanding we may gain by tackling partially-finite problems from both the finite-dimensional and infinite-dimensional sides. The comparison of these two approaches is informative, as both proofs are constructive.

Stabilizing multi-steered articulated vehicles in backward motion is a complex task for any human driver. Unless the vehicle is accurately steered, its structurally unstable joint-angle kinematics during reverse maneuvers can cause the vehicle segments to fold and enter a jack-knife state. In this work, a model predictive path-following controller is proposed enabling automatic low-speed steering control of multi-steered articulated vehicles, comprising a car-like tractor and an arbitrary number of trailers with passive or active steering. The proposed path-following controller is tailored to follow nominal paths that contains full state and control-input information, and is designed to satisfy various physical constraints on the vehicle states as well as saturations and rate limitations on the tractor's curvature and the trailer steering angles. The performance of the proposed model predictive path-following controller is evaluated in a set of simulations for a multi-steered 2-trailer with a car-like tractor where the last trailer has steerable wheels.

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.

We perform an effectivization of classical results concerning universal coding and prediction for stationary ergodic processes over an arbitrary finite alphabet. That is, we lift the well-known almost sure statements to statements about Martin-L"of random sequences. Most of this work is quite mechanical but, by the way, we complete a result of Ryabko from 2008 by showing that each universal probability measure in the sense of universal coding induces a universal predictor in the prequential sense. Surprisingly, the effectivization of this implication holds true provided the universal measure does not ascribe too low conditional probabilities to individual symbols. As an example, we show that the Prediction by Partial Matching (PPM) measure satisfies this requirement. In the almost sure setting, the requirement is superfluous.

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.

When it comes to the music scene in the midst of the coronavirus pandemic, the math is pretty simple: No shows equals no revenue.…

When he was putting together the latest compilation CD for his label CorpoRAT Records, Kris Martin had intended to hand out promotional discs at Boise's Treefort Music Festival, where several artists from the Spokane label were scheduled to perform, and then officially release the album in April for Record Store Day.…

Perhaps you've heard people banging on pans to support health care workers, or howling into the abyss just to let other humans know they were alive. We've gone to some extreme measures to keep ourselves entertained since much of the country went on lockdown to combat COVID-19, and here's another one that can get you out of the house while remaining safely social-distanced and supporting local artists at the same time.…

An apparatus for selecting a motion signifying artificial feeling is provided. The apparatus includes: an feeling expression setting unit configured to set probabilities of each feeling expression behavior performed for each expression element of a robot for each predetermined feeling; a behavior combination generation unit configured to generate at least one behavior combination combined by randomly extracting the feeling expression behaviors in each expression element one by one; and a behavior combination selection unit configured to calculate an average for the probabilities of the feeling expression behaviors included in each behavior combination for each feeling of a robot and select behavior combinations in which the average of the probabilities of the feeling expression behaviors most approximates the predetermined feeling value of a robot from each behavior combination.

A method of identifying one or more particular images from an image collection, includes indexing the image collection to provide image descriptors for each image in the image collection such that each image is described by one or more of the image descriptors; receiving a query from a user specifying at least one keyword for an image search; and using the keyword(s) to search a second collection of tagged images to identify co-occurrence keywords. The method further includes using the identified co-occurrence keywords to provide an expanded list of keywords; using the expanded list of keywords to search the image descriptors to identify a set of candidate images satisfying the keywords; grouping the set of candidate images according to at least one of the image descriptors, and selecting one or more representative images from each grouping; and displaying the representative images to the user.

A method of forming a product from an oil feedstock, such as a biodiesel product, and a heterogeneous catalyst system used to form said product is disclosed. This catalyst system, which has a high tolerance for the presence of water and free fatty acids (FFA) in the oil feedstock, may simultaneously catalyze both the esterification of FAA and the transesterification of triglycerides present in the oil feedstock. The catalyst system is comprised of a mixture of zinc oxide and a second metal oxide. The zinc oxide includes a mixture of amorphous zinc oxide and zinc oxide nanocrystals, the zinc nanocrystals having a mean grain size between about 20 and 80 nanometers with at least one of the nanocrystals including a mesopore having a diameter of about 5 to 15 nanometers. Preferably, the second metal oxide is a lanthanum oxide, the lanthanum oxide being selected as one from the group of La2CO5, LaOOH, and combinations or mixtures thereof.

The invention relates to polyglycol ether-free, polyglycerol partial ester-based sulphosuccinates, the preparation thereof, and the use of these in cosmetic formulations and also in cleaning compositions in the industrial and domestic sector and formulations comprising these sulphosuccinates.

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.

A long-fiber-reinforced resin composition including (A) a long-fiber-reinforced thermoplastic resin pellet including a thermoplastic resin, a modified polyolefin-based resin modified with an unsaturated carboxylic acid or its derivative and reinforcing fiber and satisfying (A-1) the melt index of the thermoplastic resin is 100-250 g/10 min, (A-2) the relaxation time λ of the thermoplastic resin is 0.1 (sec) or less, (A-3) the content of the reinforcing fiber is 40-70 wt %, and (A-4) the content of the modified polyolefin-based resin is 1-5 wt %; and (B) a polyolefin-based resin satisfying (B-1) the melt index of the polyolefin-based resin is 20-70 g/10 min, and (B-2) the relaxation time λ of the polyolefin-based resin is 0.23 (sec) or less; wherein the content of reinforcing fiber contained in (A) is 20-60 wt % relative to the total amount of the fiber-reinforced resin composition.

Methods for removing parasites and in particular ectoparasites of vertebrates, in particular of mammals, and compositions for the implementation of this method.Methods for removing parasites of vertebrates, and in particular arthropods, mainly insects and Arachnida, wherein an effectively parasiticidal amount of a compound of formula (I) ##STR1## in particular of fipronil, is administered to the animal via an administration route which makes possible systemic distribution and good absorption.

Methods for forming lead zirconate titanate (PZT) nanoparticles are provided. The PZT nanoparticles are formed from a precursor solution, comprising a source of lead, a source of titanium, a source of zirconium, and a mineralizer, that undergoes a hydrothermal process. The size and morphology of the PZT nanoparticles are controlled, in part, by the heating schedule used during the hydrothermal process.

A pipe choke for use in drilling and mining operations comprising a body including a first end and a second end configured to couple to a pipe, an opening extending through the body from the first end to the second end, and wherein the body includes a first phase comprising recrystallized silicon carbide and a second phase comprising silicon.

Copper(II) acetate, zinc(II) acetate, and tin(IV) acetate are weighed so that the total amount of metal ions is 2.0×10−4 mol and the molar ratio of ions is Cu:Zn:Sn=2:1:1, and 2.0 cm3 of oleylamine is added to prepare a mixed solution. Apart from this, 1.0 cm3 of oleylamine is added to 2.0×10−4 mol of sulfur powder to prepare a mixed solution. These mixed solutions are separately heated at 60° C. and mixed at room temperature. The pressure in a test tube is reduced, followed by nitrogen filling. The test tube is heated at 240° C. for 30 minutes and then allowed to stand until room temperature. The resultant product is separated into a supernatant and precipitates by centrifugal separation. The separated supernatant is filtered, methanol is added to produce precipitates. The precipitates are dissolved by adding chloroform to prepare a semiconductor nanoparticle solution.

The present disclosure relates to compositions and methods for producing nanoparticles to provide relatively more rapid delivery of such particles across the blood-brain barrier. The nanoparticles may be formed from bis-quaternary pyridinium-aldoxime salts that may also be of a specific polymorphic structure and which may be formed in either hydrophobic or hydrophilic type liquid media. In addition, the nanoparticle for transport across the blood-brain barrier may comprise a polymeric resin encapsulating a bis-quaternary pyridinium-2-aldoxime salt.

Materials and Methods are disclosed for producing nanoparticles linked to antibacterial ligands, including antibiotics and/or molecules which bind to bacterial markers, and for the use of the nanoparticles for the treatment of conditions treatable by the antibiotic ligands.

Disclosed are various embodiments of methods and systems related to stimulus responsive nanoparticles. In one embodiment includes a stimulus responsive nanoparticle system, the system includes a first electrode, a second electrode, and a plurality of elongated electro-responsive nanoparticles dispersed between the first and second electrodes, the plurality of electro-responsive nanorods configured to respond to an electric field established between the first and second electrodes.

In certain embodiments novel nanoparticles (nanowontons) are provided that are suitable for multimodal imaging and/or therapy. In one embodiment, the nanoparticles include a first biocompatible (e.g., gold) layer, an inner core layer (e.g., a non-biocompatible material), and a biocompatible (e.g., gold) layer. The first gold layer includes a concave surface that forms a first outer surface of the layered nanoparticle. The second gold layer includes a convex surface that forms a second outer surface of the layered nanoparticle. The first and second gold layers encapsulate the inner core material layer. Methods of fabricating such nanoparticles are also provided.

A process for the production of nanocrystals or amorphous nanoparticles of actives (nanomaterials), especially from the peels of grapes. A dispersion of a micrometer-sized material in a solution of surfactant or a steric stabilizer is first provided. The macrosuspension is then stirred for at least 1 minute at a rotational speed above 500 rpm using a rotor-stator mixer. The stirred mixture is passed through a jet stream or piston-gas type high pressure homogenizer. The nanomaterials produced can be incorporated into formulations for use as nutraceutical, nutritional supplement, or as supportive treatment in medical therapy. The active can be derived from the peels of grapes.

An artificial silica marble comprises a matrix and a line pattern portion. The line pattern portion comprises fine lines having a width of about 50 to about 500 μm and forms a web- or net-like pattern. The line pattern portion divides or partitions the artificial silica marble into a plurality of irregularly shaped pattern portions to form an amorphous pattern in the cross section of the artificial silica marble.

The invention provides a method and apparatus for creating plasma particles and applying the plasma particles to a liquid. Liquid feedstock (e.g., water and/or hydrocarbons mixed with biomass) is pumped through a pipeline; the single-phase stream is then transformed into a biphasic liquid-and-gas stream inside a chamber. The transformation is achieved by transitioning the stream from a high pressure zone to a lower-pressure zone. The pressure drop may occur when the stream further passes through a device for atomizing liquid. Inside the chamber, an electric field is generated with an intensity level that exceeds the threshold of breakdown voltage of the biphasic medium leading to a generation of a plasma state. Furthermore, the invention provides an energy-efficient highly adaptable and versatile method and apparatus for sanitizing water using plasma particles to inactivate biological agents contaminating water.

A treatment process of persistent organic pollutants contained in particles is provided. Said process includes reacting persistent organic pollutant in particles under hydrothermal conditions in the presence of Fe2+ and Fe3+. Several beneficial effects can be achieved, including 1) no other additive is needed during the reaction process; 2) Fe2+ and Fe3+ are safe, cheap and extensive sources; 3) because Fe2+ and Fe3+ are dissolved, they can fully disperse into particles, and fully contact can be achieved, thus obtaining a decomposition rate no less than 70% of the persistent organic pollutants is under subcritical conditions.

A process for the preparation of polymer lattices comprising polymer nanoparticles by a photo-initiated heterophase polymerization includes preparing a heterophase medium comprising a dispersed phase and a continuous phase and at least one of at least one surfactant, at least one photoinitiator, and at least one polymerizable monomer. The at least one polymerizable monomer is polymerized by irradiating the heterophase medium with electromagnetic radiation so as to induce a generation of radicals. The at least one photoinitiator is selected from compounds comprising at least one phosphorous oxide group (P═O) or at least one phosphorous sulfide (P═S) group. The irradiating of the heterophase medium is effected so that a ratio of an irradiated surface of the heterophase medium to a volume of the heterophase medium is at least 200 m−1.

A process for the preparation of modified polymers by a photo-initiated polymerization includes preparing a polymerization medium comprising at least one photoinitiator comprising at least one phosphorous oxide (P═O) group or at least one phosphorous sulfide (P═S) group, and at least one polymerizable monomer. The at least one polymerizable monomer is polymerized by irradiating the polymerization medium with electromagnetic radiation so as to induce a generation of radicals so as to obtain a polymer. The polymer is modified by irradiating the polymer with electromagnetic radiation so as to induce a generation of radicals from the polymer in a presence of at least one modifying agent.

The present invention provides a process for producing electret fine particles or coarse powder that can be uniformly electrified and exhibits excellent electrophoretic properties. Specifically, the present invention relates to the production processes (1) and (2) below:(1) A process for producing electret fine particles, comprising emulsifying a fluorine-containing material that contains a vinylidene fluoride-hexafluoropropylene-tetrafluoroethylene terpolymer in a liquid that is incompatible with the fluorine-containing material to obtain emulsified particles; and subjecting the emulsified particles to electron ray irradiation, radial ray irradiation, or corona discharge treatment.(2) A process for producing electret coarse powder, comprising subjecting a resin sheet containing a vinylidene fluoride-hexafluoropropylene-tetrafluoroethylene terpolymer to electron ray irradiation, radial ray irradiation, or corona discharge treatment to process the resin sheet into an electret resin sheet; and pulverizing the electret resin sheet.

A UV curable silicone rubber composition is provided. The composition does not undergo curing failure, foaming, and other undesirable conditions even if a water-containing inorganic filler such as zeolite were added. A UV curable silicone rubber composition comprising (A) 100 parts by weight of an organopolysiloxane having at least 2 alkenyl groups per molecule represented by the average compositional formula (I): R1aSiO(4-a)/2 (I) (wherein R1 is independently a substituted or unsubstituted monovalent hydrocarbon group, and a is a positive number of 1.95 to 2.05); (B) 1 to 300 parts by weight of an inorganic filler having a water content of at least 0.5% by weight; (C) 0.1 to 50 parts by weight of an organohydrogenpolysiloxane having at least 2 silicon-bonded hydrogen atoms per molecule; and (D) a catalytic amount of a photoactive platinum complex curing catalyst.

A method, apparatus, and system for switching from an existing target end device to a next target end device in a multi-expander storage topology by using Fast Context Switching. The method enhances Fast Context Switching by allowing Fast Context Switching to reuse or extend part of an existing connection path to an end device directly attached to a remote expander. The method can include reusing or extending at least a partial path of an established connection between an initiator and the existing target end device for a connection between the initiator and the next target end device, whereby the existing target end device and the next target end device are locally attached to different expanders.

A method for producing polymer particles includes a preparation step for preparing a first oily liquid containing an oily olefin monomer, a radical polymerization initiator, and an iodine molecule, a synthesis step for obtaining a second oily liquid containing at least an iodine compound produced by a reaction between a radical generated by cleavage of the radical polymerization initiator and the iodine molecule in the first oily liquid, a suspension step for obtaining an oil droplet of the second oily liquid by suspending the second oily liquid in water, and a polymerization step for polymerizing the oily olefin monomer in the oil droplet.

The present invention relates to a method for producing particles of a compound of interest. In a method according to the invention a solution is provided of the compound of interest in a solvent. This solution is thickened or gelled and particles are formed. The invention further relates to a particle that is obtainable by the invention.

Described is a method to prepare wet foams exhibiting long-term stability wherein colloidal particles are used to stabilize the gas-liquid interface, said particles being initially inherently partially lyophobic particles or partially lyophobized particles having mean particle sizes from 1 nm to 20 μm. In one aspect, the partially lyophobized particles are prepared in-situ by treating initially hydrophilic particles with amphiphilic molecules of specific solubility in the liquid phase of the suspension.

The disclosure relates to methods of making polymer particles, said methods including the steps of: making an aqueous gel reaction mixture; forming an emulsion having dispersed aqueous phase micelles of gel reaction mixture in a continuous phase; adding an initiator oil comprising at least one polymerization initiator to the continuous phase; and performing a polymerization reaction in the micelles. Further, the initiator oil is present in a volume % relative to a volume of the aqueous gel reaction mixture of between about 1 vol % to about 20 vol %. The disclosure also relates to methods of making nucleic acid polymer particles having the same method steps and wherein the aqueous gel reaction mixture includes a nucleic acid fragment, such as a primer.

A method of making cerium-containing metal oxide nanoparticles in non-polar solvent eliminates the need for solvent shifting steps. The direct synthesis method involves: (a) forming a reaction mixture of a source of cerous ion and a carboxylic acid, and optionally, a hydrocarbon solvent; and optionally further comprises a non-cerous metal ion; (b) heating the reaction mixture to oxidize cerous ion to ceric ion; and (c) recovering a nanoparticle of either cerium oxide or a mixed metal oxide comprising cerium. The cerium-containing oxide nanoparticles thus obtained have cubic fluorite crystal structure and a geometric diameter in the range of about 1 nanometer to about 20 nanometers. Dispersions of cerium-containing oxide nanoparticles prepared by this method can be used as a component of a fuel or lubricant additive.

Process for preparing a dispersion comprising silicon dioxide particles and cationizing agents, by dispersing 50 to 75 parts by weight of water, 25 to 50 parts by weight of silicon dioxide particles having a BET surface area of 30 to 500 m2/g and 100 to 300 μg of cationizing agent per square meter of the BET surface area of the silicon dioxide particles, wherein the cationizing agent is obtainable by reacting at least one haloalkyl-functional alkoxysilane, hydrolysis products, condensation products and/or mixtures thereof with at least one aminoalcohol and water; and optionally removing the resulting hydrolysis alcohol from the reaction mixture. Also the process for preparing the dispersion, wherein the cationizing agent comprises one or more quaternary, aminoalcohol-functional, organosilicon compounds of formula III and/or condensation products thereof, wherein Ru and Rv are independently C2-4 alkyl group, m is 2-5 and n is 2-5.

According to the present invention, a metal nanoparticle dispersion suitable to multiple layered coating by jetting in the form of fine droplets is prepared by dispersing metal nanoparticles having an average particle size of 1 to 100 nm in a dispersion solvent having a boiling point of 80° C. or higher in such a manner that the volume percentage of the dispersion solvent is selected in the range of 55 to 80% by volume and the fluid viscosity (20° C.) of the dispersion is chosen in the range of 2 mPa·s to 30 mPa·s, and then when the dispersion is discharged in the form of fine droplets by inkjet method or the like, the dispersion is concentrated by evaporation of the dispersion solvent in the droplets in the course of flight, coming to be a viscous dispersion which can be applicable to multi-layered coating.

A system and method for controlling restarting of instruction fetching using speculative address computations in a processor are provided. The system includes a predicted target queue to hold branch prediction logic (BPL) generated target address values. The system also includes target selection logic including a recycle queue. The target selection logic selects a saved branch target value between a previously speculatively calculated branch target value from the recycle queue and an address value from the predicted target queue. The system further includes a compare block to identify a wrong target in response to a mismatch between the saved branch target value and a current calculated branch target, where instruction fetching is restarted in response to the wrong target.

Systems, Apparatus, methods, and computer program products are provided for converting an existing artifact to one or more new artifacts. For example, in one embodiment, a computing device can receive input identifying an existing artifact for conversion to one or more new artifacts. One or more items from the existing artifact and their respective types can be identified for conversion. Then, the one or more items of the existing artifact can be converted to one or more new artifacts.

A method for recommending at least one artifact to an artifact user is described. The method includes obtaining user characteristic information reflecting preferences, particular to the artifact user, as to a desired artifact. The method also includes obtaining first metadata about each of one or more candidate artifacts, and scoring, as one or more scored artifacts, each of the one or more candidate artifacts by evaluating one or more criteria, not particular to the artifact user, applied to the first metadata. The method further includes scaling, as one or more scaled artifacts, a score of each of the one or more scored artifacts, by evaluating the suitability of each of the one or more scored artifacts in view of the user characteristic information. The method lastly includes recommending to the artifact user at least one artifact from among the one or more scaled artifacts based on its scaled score.

Absorbent articles provided with an odor control system. The odor control system includes at least two classes of odor control materials, wherein one class acts on malodors or a malodorous substance in the absorbent article and a second class acts on nose receptors. The classes of odor control materials may be selected to provide a synergistic effect in terms of malodor reduction.

A process for making particles comprising a hydrophobic dopant for subsequent release therefrom is disclosed. The process comprises providing an emulsion comprising a hydrophilic phase and a hydrophobic phase dispersed in the hydrophilic phase, and reacting the precursor material to form the particles comprising the dopant therein. The hydrophobic phase comprises a precursor material and the dopant.

A method for isolating 2,2,4,4-tetramethyl-1,3-cyclobutanediol (TMCD) solids from an isolated feed slurry formed in a TMCD process comprising TMCD, a liquid phase, and impurities by (a) treating the isolated feed slurry in a product isolation zone to produce an isolated TMCD product wet cake, a mother liquor, and impurities; wherein the product isolation zone can comprise at least one rotary pressure drum filter.

In a method for fracturing or mask data preparation or mask process correction for charged particle beam lithography, a plurality of shots are determined that will form a pattern on a surface, where shots are determined so as to reduce sensitivity of the resulting pattern to changes in beam blur (βf). In some embodiments, the sensitivity to changes in βf is reduced by varying the charged particle surface dosage for a portion of the pattern. Methods for forming patterns on a surface, and for manufacturing an integrated circuit are also disclosed, in which pattern sensitivity to changes in βf is reduced.

A method for mask data preparation or mask process correction is disclosed in which a set of charged particle beam shots is determined which is capable of forming a pattern on a surface, wherein critical dimension uniformity (CDU) of the pattern is optimized. In some embodiments the CDU is optimized by varying at least two factors. In other embodiments, model-based techniques are used. In yet other embodiments, the surface is a reticle to be used in an optical lithographic process to form a pattern on a wafer, and CDU on the wafer is optimized.

A method and system for optical proximity correction (OPC) is disclosed in which a set of shaped beam shots is determined which, when used in a shaped beam charged particle beam writer, will form a pattern on a reticle, where some of the shots overlap, where the pattern on the reticle is an OPC-corrected version of an input pattern, and where the sensitivity of the pattern on the reticle to manufacturing variation is reduced. A method for fracturing or mask data preparation is also disclosed.