Abstract: Techniques are provided for encoding an extended image such that it is backwards compatible with existing decoding devices. An extended image format is defined such that the extended image format is consistent with an existing image format over the full range of the existing image format. Because the extended image format is consistent with the existing image format over the full range of the existing image format, additional image information that is included in an extended image can be extracted from the extended image. A base version of an image (expressed using the existing image format) may be encoded in a payload portion and the extracted additional information may be stored in a metadata portion of a widely supported image file format.

Abstract: Techniques are provided for encoding an extended image such that it is backwards compatible with existing decoding devices. An extended image format is defined such that the extended image format is consistent with an existing image format over the full range of the existing image format. Because the extended image format is consistent with the existing image format over the full range of the existing image format, additional image information that is included in an extended image can be extracted from the extended image. A base version of an image (expressed using the existing image format) may be encoded in a payload portion and the extracted additional information may be stored in a metadata portion of a widely supported image file format.

Abstract: Techniques are provided for encoding an extended image such that it is backwards compatible with existing decoding devices. An extended image format is defined such that the extended image format is consistent with an existing image format over the full range of the existing image format. Because the extended image format is consistent with the existing image format over the full range of the existing image format, additional image information that is included in an extended image can be extracted from the extended image. A base version of an image (expressed using the existing image format) may be encoded in a payload portion and the extracted additional information may be stored in a metadata portion of a widely supported image file format.

Abstract: Techniques are provided for encoding an extended image such that it is backwards compatible with existing decoding devices. An extended image format is defined such that the extended image format is consistent with an existing image format over the full range of the existing image format. Because the extended image format is consistent with the existing image format over the full range of the existing image format, additional image information that is included in an extended image can be extracted from the extended image. A base version of an image (expressed using the existing image format) may be encoded in a payload portion and the extracted additional information may be stored in a metadata portion of a widely supported image file format.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: The present invention provides prodrugs of GABA analogs, pharmaceutical compositions of prodrugs of GABA analogs and methods for making prodrugs of GABA analogs. The present invention also provides methods for using prodrugs of GABA analogs and methods for using pharmaceutical compositions of prodrugs of GABA analogs for treating or preventing common diseases and/or disorders.

Abstract: The reactivity of a number of p-methylphenyl thioglycoside (STol) donors which are either fully protected or have one hydroxyl group exposed has been quantitatively determined by HPLC in conjunction with the development of a broadly applicable approach for a facile one-pot synthesis of oligosaccharides. The influence on reactivity of the structural effects of different monosaccharide cores and different protecting groups on each glycoside donor is characterized and quantified. In addition, a correlation between glycosyl donor reactivity and the chemical shift of the anomeric proton by 1 H NMR has been established. A database of thioglycosides as glycosyl donors has been created using this reactivity data. The utility is demonstrated by the easy and rapid one-pot assembly of various linear and branched oligosaccharide structures.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: The reactivity of a number of p-methylphenyl thioglycoside (STol) donors which are either fully protected or have one hydroxyl group exposed has been quantitatively determined by HPLC in conjunction with the development of a broadly applicable approach for a facile one-pot synthesis of oligosaccharides. The influence on reactivity of the structural effects of different monosaccharide cores and different protecting groups on each glycoside donor is characterized and quantified. In addition, a correlation between glycosyl donor reactivity and the chemical shift of the anomeric proton by 1H NMR has been established. A database of thioglycosides as glycosyl donors has been created using this reactivity data. The utility is demonstrated by the easy and rapid one-pot assembly of various linear and branched oligosaccharide structures.