The invention relates to an encoder and a decoder and methods therein for supporting split gain shape vector encoding and decoding. The method performed by an encoder, where the encoding of each vector segment is subjected to a constraint related to a maximum number of bits, BMAX, allowed for encoding a vector segment. The method comprises, determining an initial number, Np—init, of segments for a target vector x; and further determining an average number of bits per segment, BAVG, based on a vector bit budget and Np—init. The method further comprises determining a final number of segments to be used, for the vector x, in the gain shape vector encoding, based on energies of the Np—init segments and a difference between BMAX and BAVG. The performing of the method enables an efficient allocation of the bits of the bit budget over the target vector.

An input buffer for an ADC is provided. The input buffer includes a receiving circuit and an impedance circuit. The receiving circuit is coupled between a power supply and a sample-and-hold circuit of the ADC, and receives an analog input signal and generating an analog signal. The impedance circuit is coupled to the receiving circuit, and selectively provides a variable impedance. When the sample-and-hold circuit of the ADC is operated in a first phase, the impedance circuit provides a small impedance, and when the sample-and-hold circuit of the ADC is operated in a second phase, the impedance circuit provides a large impedance.

A multi-level DAC includes first and second level resistor ladders, and a dual-switch ladder interconnect reduces DNL at tap-point transitions between first-level ladder resistors. For each first level resistor N, the switch-interconnect network includes dual (first/second) switches connectable to a resistor-top node NT, and dual (third/fourth) switches selectively connectable to a resistor-bottom node NB. The first switch is operable to connect NT to a top tap switch operable to select NT as a top tap point, and the fourth interconnect switch is operable to connect NB to a bottom tap switch operable to select NB as a bottom tap point. The first and fourth switches are connected, forming an outer loop that includes top and bottom tap points. The second switch connects to a top second-level resistor RT, and the third switch connects to a bottom second-level resistor RB, forming an inner loop that includes the series-connected second-level resistors.

A digital-to-analog converter (DAC) and a high-voltage tolerance circuit are provided. The DAC includes a high-voltage tolerance circuit. The high-voltage tolerance circuit is configured to generate a reference voltage, and select the reference voltage or a first power-source voltage to control the node voltage of each branch of an operational amplifier circuit of the high-voltage tolerance circuit according the logical signal level of an input signal.

An ultrasound device including an asynchronous successive approximation analog-to-digital converter and method are provided. The device includes at least one ultrasonic transducer, a plurality of asynchronous successive-approximation-register (SAR) analog-to-digital converters (ADC) coupled to the at least one ultrasonic transducer, at least one asynchronous SAR in the plurality having a sample and hold stage, a digital-to-analog converter (DAC), a comparator, and control circuitry, wherein a DAC update event following at least one bit conversion is synchronized to a corresponding DAC update event of at least one other ADC in the plurality of ADCs.

Methods and systems for time interleaved analog-to-digital converter timing mismatch calibration and compensation may include receiving an analog signal on a chip, converting the analog signal to a digital signal utilizing a time interleaved analog-to-digital-converter (ADC), and reducing a blocker signal that is generated by timing offsets in the time interleaved ADC by estimating complex coupling coefficients between a desired digital output signal and the blocker signal utilizing a decorrelation algorithm on frequencies within a desired frequency bandwidth. The decorrelation algorithm may comprise a symmetric adaptive decorrelation algorithm. The received analog signal may be generated by a calibration tone generator on the chip. An aliased signal may be summed with an output signal from a multiplier. The complex coupling coefficients may be determined utilizing the decorrelation algorithm on the summed signals. A multiplier may be configured to cancel the blocker signal utilizing the determined complex coupling coefficients.

A hybrid SAR-ADC that uses a combination of voltage-based signal processing and time-based signal processing to convert an analog input signal to a digital output signal is disclosed. In some embodiments, the hybrid SAR-ADC has a voltage-based signal processing element configured to convert an analog input signal to a first digital signal having a plurality of MSBs and to generate a residue voltage from an input voltage and the first digital signal. A voltage-to-time conversion element is configured to convert the residue voltage to a time domain representation. A time-based signal processing element is configured to convert the time domain representation to a second digital signal comprising a plurality of LSBs. By determining the plurality of MSBs using voltage-based signal processing and determining the plurality of LSBs using time-based signal processing, the hybrid SAR-ADC is able to achieve low power and compact area.

A converter includes: a terminal that receives code-modulated power that has been generated with a modulation code; and a circuit that intermittently converts the code-modulated power with a conversion code based on the modulation code. The code-modulated power is alternating-current power.

For analog-to-digital converters (ADCs) which utilize a feedback digital-to-analog converter (DAC) for conversion, the final analog output can be affected or distorted by errors of the feedback DAC. A digital measurement technique can be implemented to determine timing mismatch error for the feedback DAC in a continuous-time delta-sigma modulator (CTDSM) or in a continuous-time pipeline modulator. The methodology utilizes cross-correlation of each DAC unit elements (UEs) output to the entire modulator output to measure its timing mismatch error respectively. Specifically, the timing mismatch error is estimated using a ratio based on a peak value and a value for the next tap in the cross-correlation function. The obtained errors can be stored in a look-up table and fully corrected in digital domain or analog domain.

For analog-to-digital converters (ADCs) which utilize a feedback digital-to-analog converter (DAC) for conversion, the final analog output can be affected or distorted by errors of the feedback DAC. A digital measurement technique can be implemented to determine switching mismatch error for the feedback DAC in a continuous-time delta-sigma modulator (CTDSM) or in a continuous-time pipeline modulator. The methodology forces each DAC unit elements (UEs) to switch a certain amount times and then use the modulator itself to measure the errors caused by those switching activities respectively. The obtained errors can be stored in a look-up table and fully corrected in digital domain or analog domain.

Typically, complex systems require a separate and expensive equalizer at the output of an analog-to-digital converter (ADC). Rather than providing a separate equalizer, the effective Signal Transfer Function (STF) of a Multi-stAge noise SHaping (MASH) ADC can be modified by leveraging available digital filtering hardware necessary for quantization noise cancellation. The modification can involves adding calculations in the software previously provided for computing digital quantization noise cancellation filter coefficients, where the calculations are added to take into account equalization as well. As a result, the signal transfer function can be modified to meet ADC or system-level signal-chain specifications without additional equalization hardware. The method is especially attractive for high-speed applications where magnitude and phase responses are more challenging to meet.

Modifying a digital data stream that includes immediately consecutive code words of different length by segmenting, based on a certain block grid, the digital data stream. Each block of the block grid includes a fixed number of bits. It is determined whether all bits of the last block associated with the digital data stream are occupied by data of the digital data stream. If not all bits of the last block are occupied, the unoccupied bits of the last block are padded with bits of an end-of-record (EOR) indicator. If all bits of the last block are occupied, attaching an EOR indicator to the digital data stream is skipped.

The present invention relates to a modular photoelectric-switch keyboard key, including modular photoelectric switch, base, keymodule and elastic element, the said modular photoelectric switch is mounted in the said base, the said keymodule is slideably placed in the sliding cavity of the said base and the said elastic element is placed between the said base and the said keymodule; the said modular photoelectric switch comprises transmitting tube, receiving tube and distance piece, the said transmitting tube and the said receiving tube are placed oppositely and are electrically connected with the circuit board; the said distance piece is connected with the said keymodule and located between the said transmitting tube and the said receiving tube.

Continuous-time analog-to-digital converters (ADCs) such as continuous-time delta-sigma ADCs and continuous-time pipeline ADCs, has input resistor structure at the input. The input resistor structure is typically tunable, and the tunability is usually provided by metal-oxide semiconductor field effect transistor (MOSFET) switches. Core MOSFETs, which has a terminal-to-terminal voltage

For continuous-time multi-stage noise shaping analog-to-digital converters (CT MASH ADCs), quantization noise cancellation often requires accurate estimation of transfer functions, e.g., a noise transfer function of the front end modulator and a signal transfer function of the back end modulator. To provide quantization noise cancellation, digital quantization noise cancellation filters adaptively tracks transfer function variations due to integrator gain errors, flash-to-DAC timing errors, as well as the inter-stage gain and timing errors. Tracking the transfer functions is performed through the direct cross-correlation between the injected maximum length linear feedback shift registers (LFSR) sequence and modulator outputs and then corrects these non-ideal effects by accurately modeling the transfer functions with programmable finite impulse response (PFIR) filters.

An analog-to-digital converter (ADC) is a device that can include a reference shuffler and a loop filter. An ADC can achieve better performance with incremental adjustment of a pointer of the reference shuffler, changing coefficients of the loop filter, and storing calibration codes of the ADC in a non-volatile memory. By incrementally adjusting a pointer of the reference shuffler, a calibration can be performed more efficiently than with a random adjustment of the pointer. By temporarily changing the loop filter coefficients, a greater amount of activity can be introduced into the loop filter. This activity can allow the calibration to proceed more efficiently. By storing the calibration codes in a non-volatile memory, a search space for calibration codes can be reduced. Thus, a calibration can occur more quickly, and the calibration itself can be improved.

An analog to digital converter includes an error integration circuit configured to receive an input charge from a detector and to integrate a difference between the input charge and one or more feedback charge pulses to create an error voltage. A quantizer is in operable communication with the error integration circuit and is responsive to the created error voltage. An accumulator having a mantissa component and a radix component is in operable communication with the quantizer. A charge feedback device in operable communication with the quantizer and the radix component of the accumulator. The charge feedback device is configured to generate the one or more feedback charge pulses proportional to the radix component of the accumulator and an output of the quantizer. Digital focal plane read out integrated circuits including the analog to digital converter are also disclosed.

A probabilistic digitizer for extracting information from a Josephson comparator is disclosed. The digitizer uses statistical methods to aggregate over a set of comparator readouts, effectively increasing the sensitivity of the comparator even when an input signal falls within the comparator's gray zone. Among other uses, such a digitizer may be used to discriminate between states of a qubit.

The disclosure relates to a circuit for stabilizing a digital-to-analog converter reference voltage. One example embodiment is a circuit for stabilizing a voltage on a reference node. The circuit includes a digital-to-analog converter that includes an array of capacitors and arranged for: receiving an input voltage via an input node, receiving a voltage via a reference node and a digital-to-analog code via a controller node, and outputting a digital-to-analog output voltage. The circuit also includes a capacitive network on the reference node comprising a fixed capacitor arranged to be pre-charged to an external reference voltage and a variable capacitor arranged to be pre-charged to an external auxiliary voltage. Further, the circuit includes a measurement block. In addition, the circuit includes a calibration block arranged for determining an updated setting of the variable capacitor based on the digital-to-analog code and the measured voltage on the reference node.

For continuous-time multi-stage noise shaping analog to digital converters (CT MASH ADCs), quantization noise cancellation often requires estimation of transfer functions, e.g., a noise transfer function of the front end modulator. To estimate the noise transfer function, a dither signal can be injected in the front end modulator. However, it is not trivial how the dither signal can be injected, since the dither signal can potentially leak to the back end modulator and cause overall noise degradation. To address some of these issues, the dither signal is injected post the flash analog to digital converter (ADC) of the front end modulator. Furthermore, dummy comparator structures can be used to synchronize the dither with the quantization noise of the targeted flash ADC.

A circuit and a method for converting an analog signal to a digital value representation is disclosed. In one aspect, the circuit includes an incremental sigma-delta analog-to-digital converter (ADC). The circuit further includes a first input line for providing a primary analog signal representing a sensor measurement to the incremental sigma-delta ADC. The circuit further includes a second input line for providing a secondary analog signal to the incremental sigma-delta ADC. The incremental sigma-delta ADC receives the primary and secondary analog signals during a first period (TADC1) and a second period (TADC2), respectively. The circuit further includes a filter configured to weight the digital values in a sequence of digital values output by the incremental sigma-delta ADC, and to output a single digital value representing the sensor measurement.

System and methods for input path matching in pipelined continuous-time Analog-to Digital Converters (ADCs), including pipelined Continuous-Time Delta Sigma Modulator (CTDSM) based ADCs, includes an input delay circuit disposed in a continuous-time input path from an input of an analog input signal to a first summing circuit of the continuous-time ADC. At least one digital delay line is disposed between an output of an earlier stage sub-ADC (of a plurality of pipelined sub-ADCs) and a sub-digital-to-analog converter (DAC) that is coupled to the first summing circuit, and between the earlier stage sub-ADC and a digital noise cancellation filter. The digital delay line(s) is configured to enable calibration of delay of output of the earlier stage sub-ADC provided to the sub-DAC and the digital noise cancellation filter in accordance with process variations of the input delay match circuit to minimize residue output at first summing circuit.

A system of systems to monitor data for carbon flux, for example, at scales capable of managing regional net carbon flux and pricing carbon financial instruments is disclosed. The system of systems can monitor carbon flux in forests, soils, agricultural areas, body of waters, flue gases, and the like. The system includes a means to identify and quantify sources of carbon based on simultaneous measurement of isotopologues of carbon dioxide, for example, industrial, agricultural or natural sources, offering integration of same in time and space. Carbon standards are employed at multiple scales to ensure harmonization of data and carbon financial instruments.

A liquid separator system having a gas phase zone, an aqueous phase zone and a denser liquid zone is used to separate mixtures of fluids. The separator can be used for separating molten sulfur from liquid redox solution or reslurry water. The system includes a vessel with a top part and a bottom part. The vessel has a larger diameter at the top part than at the bottom part. The system also includes an inlet for introducing a redox solution or reslurry water and molten sulfur, which is denser than redox solution or reslurry water, into the vessel. An outlet near the bottom part of the vessel allows a flow of the molten sulfur from the vessel. An interface control structure senses an interface level between the redox solution or reslurry water and the molten sulfur, and the interface control structure controls the flow of molten sulfur from the outlet. The interface control structure is adjusted to optimally alter the vertical height of the interface level within the vessel so that the residence time of the molten sulfur in the vessel does not decrease as the sulfur production throughput decreases, and so that the interface area of the molten sulfur and the redox solution is reduced as the sulfur throughput decreases. A pressure controller monitors the pressure in the vessel and adds or removes gas from a gas phase zone in the vessel to maintain a predetermined pressure regardless of the vertical height of the interface.

Method for producing a uranium concentrate in the form of solid particles, by precipitation from a uranium-containing solution using a precipitating agent, in a vertical reactor comprising a base, a top, a central part, an upper part, and a lower part, the solid particles of the uranium concentrate forming a fluidized bed under the action of a rising liquid current which circulates from the base towards the top of the reactor successively passing through the lower part, the central part and the upper part of the reactor, and which is created by introducing a liquid recycling current (flow) at the base of the reactor, said liquid recycling current being tapped at a first determined level (A) in the upper part of the reactor and sent back without settling to the base of the reactor, excess liquid being also evacuated via an overflow located at a second determined level (B) in the upper part of the reactor; a method in which the upper limit (C) of the fluidized bed of solid particles is controlled so that it is positioned at a level below the first and second determined levels.

The invention provides a process comprising: a crystallization step of concentrating and crystallizing the ammonium salt of sulfuric acid from an aqueous solution that contains the ammonium salt of sulfuric acid; a solid-liquid separation step of solid-liquid separating the ammonium salt of sulfuric acid obtained in the crystallization step, and a crystallization mother liquid recycling step of recycling a crystallization mother liquid obtained in the solid-liquid separation step to at least one step selected from the crystallization step and one or more steps that precede the crystallization step, in which not all of the crystallization mother liquid is recycled.

A method of producing a titanium dioxide pigment is provided. Also provided is a method of improving the processability of titanium dioxide particles without adversely affecting the rheological properties of the titanium dioxide particles.

Method and apparatus for limiting absorption of food products in specific parts of the digestive system is presented. A gastrointestinal implant device is anchored in the pyloric portion of the gastrointestinal system and extends beyond the ligament of Treitz. All food exiting the stomach is funneled through the device. The gastrointestinal device includes an anchor for anchoring the device in the pyloric portion and a flexible sleeve that extents into the duodenum. The anchor is collapsible for endoscopic delivery and removal.

A method of processing bundles of carbon nanotubes (CNTs). Bundles of CNTs are put into a solution and unbundled using sonication and one or more surfactants that break apart and disperse at least some of the bundles into the solution such that it contains individual semiconducting CNTs, individual metallic CNTs, and remaining CNT bundles. The individual CNTs are separated from each other using agarose bead column separation using sodium dodecyl sulfate as a surfactant. Remaining CNT bundles are then separated out by performing density-gradient ultracentrifugation.

Mineral, cosmetic, pharmaceutical, agricultural, nutraceutical, and other compositions are produced using a mineral composition containing minimal concentrations of cadmium, lead, arsenic, and mercury and containing relatively high concentrations of micro and macro mineral elements, of rare earth elements, of calcium, and of silica. The mineral concentrations are produced by processing naturally occurring clay soil to concentrate mineral elements naturally occurring in the soil.

A method for growing crystals in solution is suitable for the rapid, controlled and effective preparation of crystals of large dimensions from a solution supersaturated with a compound. The crystal growth is carried out under static conditions. To do this: the growth is performed in a crystallization chamber kept at a constant temperature Tc, which chamber is in fluid communication with a saturation chamber at a temperature Ts, similarly constant and different from Tc, with solubility of the compound at the temperature Ts greater than the solubility of the compound at the temperature Tc. A continuous circulation of the solution between the crystallization and saturation chambers is established, thus maintaining a constant supersaturation rate within the crystallization chamber. Furthermore, the circulating solution is subjected to a treatment for eliminating and inhibiting the formation of aggregates, enabling the nucleation of parasitic crystallites to be inhibited.

The invention provides a process for increasing the crystallinity of at least one solid material which is less than 100% crystalline, comprising applying ultrasound to the substantially dry solid material.

The present invention relates to compositions and methods to increase the output of a high quality product from the precipitation liquor crystallization process exemplified through the aluminum hydroxide recovery processes such as the Bayer process. The invention is a method of increasing the size of precipitates from a liquor. The invention in one embodiment relates to the use of a crystal growth modifier compositions added to the precipitation process to increase the particle size distribution of the precipitated alumina trihydrate.

A system and a method are provided that take a potentially dangerous waste product and process the product to create a marketable asset. The system and method are configured to create “tb” from “tbgs” by removing the volatility that exists in the “tbgs.” The resultant “tb” may be substantially non-volatile.

An object of the present invention is to provide a method for producing composite carbon fibers in which two or more carbon fibers are dispersed in a nearly homogenous state, the composite carbon fibers capable of being easily dispersed in a matrix such as a resin without leaving aggregate, and imparting low resistance. Disclosed is a method for producing composite carbon fibers, which comprises imparting a cavitation effect to slurry containing 6% by mass or less of two or more carbon fibers each having a different average fiber diameter under a pressure of 100 MPa or more and less than 245 MPa thereby to form a composite.

Titanium dioxide which includes particles having a large major-axis length in a large proportion and comprises columnar particles having a satisfactory particle size distribution. A titanium compound, an alkali metal compound, and an oxyphosphorus compound are heated/fired in the presence of titanium dioxide nucleus crystals having an aspect ratio of 2 or higher to grow the titanium dioxide nucleus crystals. Subsequently, a titanium compound, an alkali metal compound, and an oxyphosphorus compound are further added and heated/fired in the presence of the grown titanium dioxide nucleus crystals. Thus, titanium dioxide is produced which comprises columnar particles having a weight-average major-axis length of 7.0-15.0 μm and in which particles having a major-axis length of 10 μm or longer account for 15 wt. % or more of all the particles.

Provided is a method and an apparatus for purifying potassium nitrate from the solid waste produced by a chemical glass-strengthening process. In the method, the solid waste is melted into a liquid waste at first. Potassium nitrate of various purity grades can be obtained by batch processing the liquid waste through stepwise cooling processes of cooling the liquid waste to a first temperature facilitating the potassium nitrate contained in the liquid waste to be crystallized at a first rate and then cooling the liquid waste to a second temperature close to the freezing point of the potassium nitrate at a second rate that is slower than the first rate. The recovered potassium nitrate from the solid waste can be recycled and reused.

A process is provided for preparing a salt product with reduced sodium content including the step of providing a concentrated brine, which is typically seawater, to which has been added potassium chloride. The mixture is transferred to a crystallizer unit where at least a portion of the mix is transferred to the crystallizer through a washing column. Liquid is evaporated from the crystallizer such that crystals form, crystals are passed from the crystallizer through said washing column to a separating unit such that in the passing through the washing column the crystals are rinsed with the brine portion being transferred as a counter current through the column. The inventive process is characterized by recycling of the brine from which the salt crystallizes, thus all main ingredients of the mixed input brine reach a steady equilibrium concentration in the mother liquor in the crystallizer. These will then precipitate as crystals, as more of the respective substances gets added to the mother liquor through inflow of mixed input brine. None of the liquor is purged out of the system as in conventional salt crystallizers. All the components in the feed are substantially contained in the product from the crystallizer either as crystalline material or soluble ingredients.

An energy harvesting device includes: a first nanoporous electrode and a second nanoporous electrode, each of which is configured to which store electrical charge; a first current collector connected to the first nanoporous electrode and a second current collector connected to the second nanoporous electrode; and an enclosure that contains the first and second nanoporous electrodes and the first and second current collectors and transfers a force applied from the outside to the first nanoporous electrode and the second nanoporous electrode, wherein at least one of the first nanoporous electrode and the second nanoporous electrode comprises an ion conductive polymer.

An elastic wave device including a substrate, an interdigital transducer (IDT) electrode provided on an upper surface of the substrate, a first wiring electrode provided on the upper surface of the substrate and connected to the IDT electrode, a dielectric film that does not cover a first region of the first wiring electrode but covers a second region of the first wiring electrode above the substrate, the first wiring electrode including a cutout in the second region, and a second wiring electrode that covers an upper surface of the first wiring electrode in the first region and an upper surface of the dielectric film in the second region above the substrate.

Provided is a garment generating electricity which transforms kinematic energy generated when a user wearing the garment walks and/or swings arms past torso to an electric energy, and has a simple structure and is produced at low cost, and realizes excellent electricity generation efficiency. A garment generating electricity from ambulation or aim swinging past torso or both includes a magnet member arranged on a first part of a garment to generate magnetic field, a coil member provided on a second part of the garment which reciprocally moves with the first part of the garment while walking or swinging aims past torso, the coil member generating electricity from the magnetic field of the magnet member, and a storage battery charged with the electricity generated by the coil member.

Apparatus and methods are provided for activity accessory including an energy harvester or generator. In an example, an activity accessory can include a first enclosure and an energy generator enclosed within the first enclosure. The energy generator can include a second enclosure. The energy generator can include a spherical magnet housed within the second enclosure and windings surrounding the second enclosure. Movement of the spherical magnet within the second enclosure can induce charge movement in the windings.

An object is to provide an interior permanent magnet rotor unit that allows possible demagnetization to be suppressed regardless of a material for a portion of a permanent magnet, which is positioned on an outward side in a radial direction of a core. A core is a laminate of first thin-plate-like members and second thin-plate-like members. The first thin-plate-like members and the second thin-plate-like members have first insertion slots and second insertion slots each of which is filled with a permanent magnet. In the first thin-plate-like members, a separating portion is formed at an end of each of the first insertion slots or the second insertion slots, which end is located on an outward side of the insertion slot in a radial direction, to form a slit in the corresponding permanent magnet.

The invention relates to an electric machine (10) with commutating brushes (12) and an electric interference-suppression component (14). The brushes (12) are arranged in an annular brush support (18), and the brush support (18) sits on an axial end (22) of a housing part (24) of the electric machine (10), which is preferably a pole housing (240). The interference-suppression component (14) is arranged radially outside of the housing (24), and the brush support (18) has a protrusion (30) which extends in the radial direction (2). The protrusion (30) extends radially towards the outside so as to extend outside of the housing (24), the interference-suppression component (14) being arranged on the protrusion (30).

A monolithic integration of phase change material (PCM) switches with a MEMS resonator is provided to implement switching and reconfiguration functionalities. MEMS resonator includes a piezoelectric material to control terminal connections to the electrodes. The PCM is operable between an ON state and an OFF state by application of heat, which causes the phase change material to change from an amorphous state to a crystalline state or from a crystalline state to an amorphous state, the amorphous state and the crystalline state each associated with one of the ON state and the OFF state. A method of fabricating the MEMS resonator with phase change material is provided. A reconfigurable filter system using the MEMS resonators is also provided.

An AT-cut crystal element includes a crystal element having two side surfaces (namely, a Z'-surface) intersecting with a Z-axis of a crystallographic axis thereof. At least one of the two side surfaces is constituted of three of first to third surfaces. The first to the third surfaces meeting following conditions: the first to the third surfaces intersect with one another in this order and formed by rotating a principal surface of the crystal element by predetermined angles; and expressing the angle of the first surface as θ1, a length of the first surface as D, a thickness of a part of the crystal element having the principal surface as t, and M=D/t, and a conversion percentage as fn (M, (θ1)), the θ1 and the M are set such that the conversion percentage fn (M, (θ1)) becomes a predetermined value Th or less.

A pair of notches or slits in a collar can prevent the formation of bulky crests or wrinkling when the collar is arranged in an outer open ‘continental style’ under a jacket, however there is also a propensity for such a collar to curl up at the notches. The invention herein discloses the use of a fastening means to prevent the slit borders, forming the edge surfaces of each back section of the collar, from curling up from the shirt surface. The fastener means are located on each side of the collar, such that one member is located on the inner surface of the back collar where the outside edge meets the base of the slit edge and the other member is located on the outer surface of the collar band.

A multi-layered garment may comprise components that are affixed using integrated belt loops. In particular, shorts belt loops of a shorts component may pass through an opening created when single-layer skirt belt loops of a skirt component are oriented outwards. Both the skirt belt loops and the shorts belt loops may be fully functional and aesthetically pleasing belt loops. Additionally, the shorts belt loops may be combined with the skirt belt loops to form integrated belt loops, thereby allowing a belt to pass beneath both sets of belt loops simultaneously to affix the shorts component to the skirt component.

An embodiment of a leg protector of the present disclosure includes an upper thigh pad that is structurally attached to an upper bracing shell including lateral and medial uprights. The upper shell and thigh pad can be held to the player via a strap and/or garment. The uprights extend to uni- or polycentric hinges arranged on, and in one embodiment biased against, either side of the player's knee. A connecting member extends in a frontward direction from each hinge and attaches to a patella pad held in place over the player's knee. The patella pad may additionally be connected to the thigh pad via one or more connecting strip. Each hinge is also connected to a lower bracing shell, which includes lateral and medial uprights that extend down and around the player's lower leg, anteriorly or posteriorly. The lower shell can also be fitted via a strap or garment.