|| List of recent Delta-related patents
|Serialization for delta encoding|
Data can be serialized in such a manner as to facilitate later delta encoding, even when the serialization is performed using a lossy compression algorithm or an algorithm in which portions of the serialized data are encoded relative to other portions which may be modified. This can be achieved by approaches including preserving keyframe information across modified versions of a file, duplicating information from a previously created compressed file when serializing a later version, or adding change information showing differences between versions of a file during the serialization process..
|Composition and method of synthesizing a biomolecule and its therapeutics applications|
The embodiments herein provide a therapeutic composition comprising n (delta)-protonated l-2-amino-5-diaminomethyleneamino-pentanoic acid called j factor and a method of ex-vivo synthesis of j-factor from n(omega)′-protonated l-arginine at a ph of 5-9. The method involves increasing a temperature and or decreasing an acidity of an aqueous solution containing the n(omega)′-protonated l-arginine to obtain a ph value of greater than pka−2 or less than pka+2.
|Pharmaceutical compositions and related methods|
The present disclosure relates to compositions and methods for accelerating the healing process of wounds, increasing the closure of skin wounds, and decreasing inflammation at the site of a skin wound. Specifically, the disclosure relates to compositions comprising a delta-pkc activator, an alpha-pkc inhibitor, and a pharmaceutically acceptable carrier that is free of ca2+ and mg2+ cations.
|Method for generating a digital signal|
A method is provided for generating a digital signal (ds) from an analog signal (ia, ua) generated by a frequency converter on the basis of pulse width modulation, wherein the digital signal corresponds to a mean value of the analog signal over a period of the pulse width modulation. The method includes the acts of: generating a bit stream (bs(i)) with a predetermined bit repetition duration (bw) depending on the analog signal by way of a sigma-delta modulator (1) and, during a time interval which has a duration which is at least as great as the period of the pulse width modulation: multiplying a respective bit (bs(i)) of the bit stream by a corresponding rating coefficient (bk(i)) for generating a respective bit/rating coefficient product and summing the respective bit/rating coefficient products, wherein the sum represents the digital signal..
|Method, apparatus, and system for providing and using a scheduling delta queue|
A contact center is described along with various methods and mechanisms for administering the same. Work assignment methods are disclosed that place tasks in bins by time intervals and are processed within a delta queue ring buffer.
|Analysis of variance in network page access|
Analyzing communication network data set access of a data set group constituted by multiple data sets. The method includes the following steps: (i) determining, for a first interval, a first low access count value corresponding to an amount of data sets in the data set group that have been accessed, in the first interval, an amount of times that is no greater than a low access threshold value; (ii) determining, for a second interval, a second low access count value corresponding to an amount of data sets in the data set group that have been accessed, in the second interval, an amount of times that is no greater than the low access threshold value; and (iii) determining a delta value based, at least in part, on a difference between the first low access count value and the second low access count value..
|Phase-to-amplitude converter for direct digital synthesizer (dds) with reduced and and reconstructed add logic arrays|
A sine wave generator for a direct digital synthesizer (dds) converts a digital phase input into a digital sine wave output. Sine values and slopes are stored in read-only memory (rom) for coarse upper phase bits in a first quadrant.
|Method and apparatus for speech recognition|
A computer-implemented method, apparatus and computer program product. The computer-implemented method performed by a computerized device, comprising: transforming a hidden markov model to qubits; transforming data into groups of qubits, the data being determined upon the hidden markov model and features extracted from an audio signal, the data representing a likelihood observation matrix representing likelihood of phoneme and state combinations in an audio signal; applying a quantum search algorithm for finding a maximal value of the qubits; and transforming the maximal value of the qubits into a number, the number representing an entry in a delta array used in speech recognition..
|Method of diagnosis or prognosis of a neoplasm comprising determining the level of expression of a protein in stromal cells adjacent to the neoplasm|
The invention provides diagnostic and therapeutic methods for neoplastic disease patients with neoplasms of, for example, the breast, skin, kidney, lung, pancreas, rectum and colon, prostate, bladder, epithelial, non-epithelial, lymphomas, sarcomas, melanomas, and the like, wherein the method comprises determining the level of expression o caveolin-1, caveolin-2, vimentin, calponin2, tropomyosin, gelsolin, prolyl 4-hydroxylase alpha, ef-i-delta, or m2-isoform of pyruvate kinase in stromal cells adjacent to the neoplasm.. .
|Vaginal tissue rejuvenation compositions and methods|
A method of stimulating elastin and/or collagen production in the tissues of the vagina, comprising the steps of providing a composition including at least one of a water soluble zinc salt such as zinc sulfate and a peroxisome proliferator-activated receptor beta/delta (ppar 13/8) agonist, and administering the composition to the tissue of the vagina. Compositions for stimulating 5 elastin and/or collagen production in the tissues of the vagina are also disclosed..
|Delta-pi signal acquisition|
Values representative of modulation signal components are extracted from a modulated signal. The modulated signal contains a modulation signal.
To provide a digital modulator including: a signal adjuster (105) which is provided with a plurality of output lines, and which outputs, to the output line, which corresponds to a range to which a level of an input signal belongs, a signal of a level corresponding to the level of the input signal; a plurality of internal digital modulators (111-1 to 111-n), each of which is provided so as to correspond to each of the plurality of output lines and carries out delta-sigma modulation on the signal of the corresponding output line to output the modulated signal; and an encoder (113) which encodes the plurality of modulated signals respectively outputted by the plurality of internal digital modulators.. .
|Method and apparatus for wireless image transmission to a projector|
A method and apparatus is provided in which a digital image is transmitted to a presentation projector resource over a wireless transmission medium using a reduced amount of bandwidth by transmitting a subset of the digital image data. The subset of image data may be a delta subset that represents those areas of the image that have changed since the previous transmission.
|Multiplexed sigma delta modulator|
A multiplexed sigma delta modulator constituted of: a control circuitry; a multiplexer responsive to the control circuitry and arranged to receive a plurality of input signals; a comparing circuit, a first input of the comparing circuit coupled to the output of the multiplexer; an integrator, the input of the integrator coupled to the output of the comparing circuit; a latched comparing circuit, one input of the latched comparing circuit coupled to the output of the integrator; a plurality of storage elements, each associated with one of the plurality of inputs; and a feedback circuit arranged to feedback the output of the latched comparing circuit to the second input of the comparing circuit, wherein the control circuitry is further arranged to store the charge of an element of the integrator on the associated storage element when the associated signal is not passed by the multiplexer to the output of the multiplexer.. .
|Power amplification device|
A power amplification device of the present invention includes a delta-sigma modulator which performs a multilevel delta sigma modulation on amplitude signals of input signals, a plurality of power amplifiers which amplify carrier signals, an encoder which generates a first control signal that controls on/off of the outputs from said plurality of power amplifiers in accordance with the output from said delta-sigma modulator, and a combiner which combines at least two power output from said plurality of power amplifiers in accordance with said first control signal.. .
|Delta partitions for backup and restore|
Systems and methods of using delta partitions for backup and restore are disclosed. An example method may include after a full backup, separating change information from static information.
|Auto test for delta t diagnostics in an hvac system|
An hvac controller may be programmed to initiate a delta t test in response to a request received from a user. The user may initiate the delta t test at the hvac controller or via a remote device.
|Control-based inversion for estimating a biological parameter vector for a biophysics model from diffused reflectance data|
What is disclosed is a system and method for estimating a biological parameter vector for a biophysics model using reflectance measurements obtained from a reflectance-based spectral measurement system. The present method uses a semi-empirical biophysics model to describe skin properties and estimate reflectance spectra and reduces the dimensionality of the estimated and measured reflectance spectra using basis vectors for computational efficiency.
|Methods and pharmaceutical compositions for treating lymphoid malignancy|
The present invention provides, inter alia, methods for treating, preventing, or ameliorating the effects of a lymphoid malignancy, such as those associated with a mutated phosphatase and tensin homolog (pten) gene, or t-cell acute lymphoblastic leukemia (t-all). These methods include administering to a subject an effective amount of a phosphoinositide 3-kinase-delta (pi3kδ) inhibitor and a phosphoinositide 3-kinase-gamma (pi3kγ) inhibitor.
|All-digital multi-standard transmitter architecture using delta-sigma modulators|
The present disclosure is concerned with a digital transmitter using delta-sigma modulators (dmss) that uses an up-sampler and modulator block that follows the dsms to generate the rf equivalent of the baseband signal to be transmitted. The up-sampler and modulator block is simple to implement and contains only one or a few multiplexers implemented in high speed logic technology..
|Sigma-delta converter system and method|
A sigma-delta converter may include a filter coupled to a first summation circuit and a second summation circuit. A multi bit quantizer may be coupled to the second summation circuit.
|Combinations comprising alpha-2-delta ligands|
The instant invention relates to a combination, particularly a synergistic combination, of an alpha-2-delta ligand and a dual serotonin-noradrenaline re-uptake inhibitor (dsnri) or one or both of a selective serotonin re-uptake inhibitor (ssri) and a selective noradrenaline re-uptake inhibitor (snri), and pharmaceutically acceptable salts thereof, pharmaceutical compositions thereof and their use in the treatment of pain, particularly neuropathic pain.. .
|Fiber optic cables and assemblies and the performance thereof|
A fiber optic drop cable includes an optical fiber, a tight buffer layer on the optical fiber, at least one strength member, and a jacket surrounding the tight buffer layer. The jacket is coupled to the at least one strength member by at least partial embedment of at least one of the strength members in the jacket, which facilitates coupling between the jacket and strength member.
|Rf signal generating circuit, and transmitter|
An rf signal generating circuit that generates, from a digital signal, an rf pulse signal to be radio-transmitted. It includes a polar converter generating an amplitude signal and a phase signal from the digital signal; a signal decomposer receiving the amplitude signal as an input signal, and generates two signals, a pulse width control signal and a residual signal; a delta sigma modulator subjecting the residual signal to delta-sigma modulation; a pulse width modulator subjecting the phase signal to pulse modulation in accordance with the pulse width control signal, and outputting a pulse phase signal; and a mixer that mixes a signal output from the delta sigma modulator and the pulse phase signal to output the rf pulse signal.
|Sigma-delta modulator with trimmed reference voltage for quantizer|
A sigma delta modulator includes a first circuit that receives an analog signal and provides an intermediate signal and a first quantizer signal and further includes a first quantizer that receives the first quantizer signal and provides a first quantizer output. Also included are a second input circuit that receives the intermediate signal and provides a second quantizer signal and a second quantizer that receives the second quantizer signal and provides a second quantizer output.
|Continuous data backup using real time delta storage|
A continuous data backup using real time delta storage has been presented. A backup appliance receives a backup request from a backup agent running on a computing machine to backup data on the computing machine.
|Encoding and decoding delta values|
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for encoding and decoding delta values. In one aspect, a method includes accessing a compression buffer having a start position, a sentinel position, and a data storage region; obtaining a first value; determining that a second value stored in the sentinel position does not match a first sentinel value; determining that a third value stored in the start position matches a second sentinel value; and storing the first value at the start position of the compression buffer..
|Edge determination device|
A method of determining an edge on an option strategy is disclosed. An option strategy may be accepted where the option strategy is a combination of buying and selling puts in calls.
|Method for designing band pass delta-sigma modulator, band pass delta-sigma modulator, signal processing device, and radio transceiver|
F0 is a center frequency of a quantization noise stop band of the band pass delta-sigma modulator.. .
|Delta wing unmanned aerial vehicle (uav) and method of manufacture of the same|
This disclosure pertains to the field of small-unmanned aerial vehicles (uavs). The delta wing vehicle consists of an isosceles triangular shaped lifting body milled from styrofoam.
|Axmi221z, axmi222z, axmi223z, axmi224z and axmi225z delta-endotoxin genes and methods for their use|
Compositions and methods for conferring pesticidal activity to bacteria, plants, plant cells, tissues and seeds are provided. Compositions comprising a coding sequence for a toxin polypeptide are provided.
|Dynamically self-adjusting magnetometer|
A dynamically self-adjusting magnetometer is disclosed. In one embodiment, a first sample module periodically generates an electronic signal related to at least one magnetic field characteristic of a monitored environment.
|Yeast-based compositions and methods for the treatment or prevention of hepatitis delta virus infection|
Disclosed are immunotherapeutic compositions and methods for preventing and/or treating hepatitis delta virus (hdv) infection, including yeast-based hdv immunotherapeutic compositions and methods of use of such compositions to prevent and/or treat hdv infection and symptoms and sequela thereof.. .
|Syntax and semantics for buffering information to simplify video splicing|
Innovations in syntax and semantics of coded picture buffer removal delay (“cpbrd”) values potentially simplify splicing operations. For example, a video encoder sets a cpbrd value for a current picture that indicates an increment value relative to a nominal coded picture buffer removal time of a preceding picture in decoding order, regardless of whether the preceding picture has a buffering period sei message.
|Adaptive lossy framebuffer compression with controllable error rate|
The device and method described in this application relate generally to graphics processing systems utilizing the tile based rendering technique and more specifically relate to the processing of the framebuffer data in graphics processing applications. The present invention discloses techniques to reduce the bandwidth needed to access the color data stored in the framebuffer.
An integrated-circuit, continuous-time, sigma-delta analogue-to-digital converter has a single-ended analogue input, a converter reference input, and a ground connection. The converter has a resistor-capacitor integrator arranged to receive the single-ended analogue input.
|Bicmos gate driver for class-s radio frequency power amplifier|
The invention may be embodied in a resynchronizing, push-pull drive circuit for driving the gate electrodes of a digital class-s radio frequency power amplifier (rf-pa). A binary bitstream received from a bitstream generator, such as a sigma-delta modulator, viterbi-based optimal-bit-pattern modulator sigma-delta, or other suitable modulator, is resynchronized to a low-jitter master clock, then converted to fast-rise, high-swing complementary digital signals to drive the gates of the class-s rf-pa.
|Apparatus and a method for testing winding resistances of transformers|
The present invention relates to an apparatus for measuring winding resistances of windings in a delta-connected transformer, comprising at least a first and a second dc current source (s1, s2) connected each between the phase ends of a first (a) and a second leg (c; b) respectively of the primary side (p) of the transformer and at least a third dc current source (s3) connected between two nodes (a, b) of the secondary side (s) of the transformer. Furthermore the invention relates to a method for measuring a winding resistance of windings in delta-connected transformers, comprising the steps of applying a first and a second measuring current to each one of two corresponding legs (c, b), applying a third measuring current (i2) between two nodes (b, a) of a pair of windings on the secondary side (s) and measuring at least a winding resistance of the winding between said nodes (b, a) on the secondary side (s) of the transformer and/or the winding resistance of a leg (a) of the primary side (p) as soon as an inductive voltage drop in the windings substantially equals zero..
|Semiconductor light emitting device and method for manufacturing the same|
A semiconductor light emitting device includes a first nitride semiconductor layer, a dopant doped semiconductor layer on the first nitride semiconductor layer, an active layer on the dopant doped semiconductor layer, a delta doped layer on the active layer, a superlattice structure on the delta doped layer, an undoped layer on the superlattice layer, a second nitride semiconductor layer including a first n-type dopant, a third nitride semiconductor layer including a second n-type dopant, and a fourth nitride semiconductor layer including a third n-type dopant.. .
|Extending server-based desktop virtual machine architecture to client machines|
A server-based desktop-virtual machines architecture may be extended to a client machine. In one embodiment, a user desktop is remotely accessed from a client system.
|Recombinant microbial cells that produce at least 28% eicosapentaenoic acid as dry cell weight|
Recombinant microbial cells are disclosed herein that produce an oil comprising at least 28 percent eicosapentaenoic acid (epa) measured as a weight percent of dry cell weight. These cells may comprise a polynucleotide sequence encoding an active acyl-coa:lysophosphatidylcholine acyltransferase (lpcat) comprising at least one amino acid mutation in a membrane-bound o-acyltransferase motif.
|Single-bit direct modulation transmitter|
Single-bit transmitter modulator having a digital pulse shaping filter configured to shape data pulses of an inphase signal and quadrature signal; an upsampling filter configured to increase the sample rate of the inphase signal and quadrature signal; a sigma-delta modulator providing a one-bit inphase output signal and a one-bit quadrature output signal; an inphase low-order analog low pass filter coupling the one-bit inphase output signal to an inphase channel input of a quadrature modulator, and a quadrature low-order analog low pass filter coupling the one-bit quadrature output signal to a quadrature channel input of a quadrature modulator; and, wherein the quadrature modulator is connected to a carrier signal generator and is configured to generate an inphase and quadrature modulated carrier.. .
|Delta-sigma modulation apparatus and dynamic element-matching circuit thereof|
A delta-sigma modulation apparatus and a dynamic element-matching circuit thereof are disclosed. The dynamic element-matching circuit includes a data aligner, a logic operation circuit, and a delayer.
|Fractional-n frequency synthesizer with low quantization noise|
A fractional-n frequency synthesizer with low quantization noise includes a phase frequency detector, a charge pump, a loop filter, a voltage controlled oscillator a divider and a delta-sigma modulator. The delta-sigma modulator computes “n” to the loop filter in the output current of the charge pump.
|Magnetic field sensor linearization architecture and method|
A method of processing an output signal and a readout circuit for a magnetic field sensor are disclosed. The purpose of the readout circuit is to generate a digital representation of the magnetic field vector strength.
|Nitride semiconductor light emitting device and fabrication method thereof|
Provided is a nitride semiconductor light emitting device including: a first nitride semiconductor layer; an active layer formed above the first nitride semiconductor layer; and a delta doped second nitride semiconductor layer formed above the active layer. According to the present invention, the optical power of the nitride semiconductor light emitting device is enhanced, optical power down phenomenon is improved and reliability against esd (electro static discharge) is enhanced..
|Recovery of highly pure alpha-tocotrienol from crude palm oil extract|
Disclosed is a process for the production of high purity alpha-tocotrienol from palm oil extract. More particularly, the invention relates to a process for the separation of alpha-tocotrienol from a mixtures of other tocotrienols and tocopherols and the use of a simplified separation scheme based on a combination of solid phase extraction and simulated moving bed (smb) separation steps employing polar phase simulated moving bed operation.
|Resin composition, copper-clad laminate and printed circuit board for use therewith|
A resin composition includes (a) an epoxy resin; (b) a benzoxazine (bz) resin; (c) a styrene maleic anhydride (sma) copolymer; and (d) a polyester. The resin composition includes specific ingredients of a polyester and is characterized by specific proportions thereof so as to achieve a low delta tg value of copper clad laminates manufactured in accordance with the resin composition and attain a low dielectric constant, a low dielectric dissipation factor, high heat resistance, and high fire retardation of the copper clad laminates and printed circuit boards manufactured in accordance with the resin composition..
|Three-phase capacitor formed by two aligned cylinders with overpressure disconnection|
Three-phase capacitor formed by two cylinders where each of the cylinders comprises an outer part which corresponds to a capacitor (1) and (2) while the inner part of each cylinder corresponds to a capacitor (3) and (3′) and which are connected in delta with phases (a), (b) and (c), where each capacitor is separated from the adjacent of each cylinder by means of an insulating material which allows the movement of the inner part with respect to the outer one of each cylinder in case of overpressure, which causes the breakage of the connections made in a particular manner, the breakage of the conductive coating layer (7) which connects armatures (3.1) and (1.2); the breakage of the conductive coating layer (8) which connected armatures (2.2) and (3′.2), the breakage of the connection of connection cable (6) with phase (c), serving as an effective means of protection against internal overpressures.. .
|Compensation for air gap in an input device|
Embodiments of the present invention generally provide a processing system for a display device integrated with a capacitive sensing device. The processing system includes a driver module, a receiver module, and a determination module.
|Software update service method and apparatus for mobile terminal|
A software update method and apparatus for a mobile terminal is provided. A delta generating server determines a plurality of available update versions for a currently installed version of a target software of the mobile terminal and transmits available update version information indicating available update versions to the mobile terminal.
|Utility node software/firmware update through a multi-type package|
Software and/or firmware of a utility node device may be updated by utilizing an update package that includes multiple update items related to different types of the software and/or firmware. The utility node device may selectively install one or more of the multiple update items based on a type of the software and/or firmware that is currently installed on the device.
|Main-memory database checkpointing|
The present invention extends to methods, systems, and computer program products for main-memory database checkpointing. Embodiments of the invention use a transaction log as an interface between online threads and a checkpoint subsystem.
|System, method and computer readable medium for effieicnt snapshot-based mirroring operations|
A storage system that may include a management module, a communication module and a storage module; wherein the management module is arranged to receive, at an intermediate point in time that occurs between the first point in time and a second point in time, a first request that indicates that a certain extent of the second logical volume is irrelevant; participate in a creation of second point in time snapshots of the first and second logical volumes; select, in response to the first request, out of all data deltas generated between the first and second point in time, selected data deltas to be transmitted to the other storage system; wherein the selected data deltas exclude data deltas associated with the certain extent that were generated between the first point in time and the intermediate point in time.. .
|Replication mechanisms for database environments|
Data replication in a database includes identifying a source database system. The source database includes a main index file and a delta log file.
|Device, method and system of pricing financial instruments|
Some demonstrative embodiments include methods, devices and systems of pricing financial instruments. In one embodiment, a pricing module may be configured to receive first input data corresponding to at least one parameter defining a first option on an underlying asset and second input data corresponding to at least one current market condition relating to said underlying asset, and, based on said first and second input data, to determine a price of the first option according to a volatility smile satisfying a first criterion relating to a sum of a first correction corresponding to the first option and a second correction corresponding to a second option representing a position opposite to a position of a the first option and having substantially a same absolute delta value as the first option, wherein the first correction relates to a difference between a theoretical price of the first option and the price of the first option according to the volatility smile, and wherein the second correction relates to a difference between a theoretical price of the second option and the price of the second option according to the volatility smile.
|Fuzzy controls of towed objects|
A fuzzy logic controller for controlling towed objects includes comprises a winch controller to control extension or retraction of a tow cable based on a control signal. A fuzzy logic controller controls a speed at which the tow cable is extended or retracted.
|Parasiticidal combination comprising indoxacarb and deltamethrin|
The invention relates to antiparasitic compositions comprising a combination of indoxacarb and deltamethrin and their use in a method to control parasite insect- and acarid-infestations on animals.. .
|Delta die intensity map measurement|
With an optical inspection tool, images of a plurality of patches of a plurality of dies of a reticle are obtained. The patch images are obtained so that each patch image is positioned relative to a same reference position within its respective die as another die-equivalent one of the patch images in each the other ones of the dies.
|Low power analog to digital converter|
Described is an analog to digital converter (adc) which comprises: a sigma-delta modulator to receive an analog signal, the sigma-delta modulator operable to perform chopping to cancel common-mode noise; and one or more counters coupled to the sigma-delta modulator to generate a digital code representative of the analog signal.. .
|Fast response high-order low-pass filter|
A fast-response high-order low-pass filter circuit is provided. The circuit includes a plurality of low pass filter (lpf) poles that are connected in series, a forward bypass channel that includes a first delta voltage module that conducts at a first predetermined voltage and a first impedance module that provides a first impedance and is in series with the first delta voltage module, and a reverse bypass channel that includes a second delta voltage module that conducts at a second predetermined voltage and a second impedance module that provides a second impedance and is in series with the second delta voltage module.
|Digital controllers and digital control methods of multi-phase switching converters|
A method for controlling a multi-phase switching converter with a plurality of switching circuits, including: sensing the output current of the switching circuit and generating a current sensing signal; generating a digital phase current signal based on the current sensing signal; subtracting the digital phase current signal from a current reference signal and generating a current error signal; proportionally integrating the current error signal and generating a first bias signal; conducting a sigma-delta modulation of the first bias signal and generating a second bias signal, wherein the first bias signal is a p-bit digital signal, the second bias signal is a q-bit digital signal, and p is larger than q; and adjusting a control signal controlling the switching circuit based on the second bias signal.. .
|Atomic layer deposition of high performance anti reflection coatings on delta-doped ccds|
A back-illuminated silicon photodetector has a layer of al2o3 deposited on a region of a silicon oxide surface that is left uncovered, while deposition is inhibited in another region by a contact shadow mask. The al2o3 layer is an antireflection coating.
|Generating and using temporal data partition revisions|
Concepts and technologies are disclosed herein for generating and using temporal data partition revisions. In some embodiments, a server computer can execute a data management application.
|Delta neutral futures allocation|
A method allocates quantities of an underlying financial product for a plurality of orders, each being for a quantity of a derivative financial product counter to a previously received order for the derivative financial product and characterized by a ratio of the quantity of the derivative financial product to a quantity of the underlying financial product, and includes receiving first and second orders for quantities of the derivative financial product, computing first and second quantities of the underlying financial product, based on the first and second orders to achieve the ratio, rounding the first quantity to determine a first whole number quantity, generating a composite quantity of the underlying financial product based on the first and second quantities, generating a rounded representation of the composite quantity, and determining a second whole number quantity of the underlying financial product based on the rounded representation and the first whole number quantity.. .