1. A decorative assembly, comprising:
an electrical cord terminated by at least one electrical connector;
a first lighting element;
a first lighting element socket electrically coupled to the electrical cord and dimensioned and arranged to retain and make mating electrical contact with the first lighting element; and
a fragrance releasing cartridge coupled to at least one of the first lighting element socket and the first lighting element, said cartridge having at least one of a first section defining an interior bore dimensioned and arranged to receive and retain an upper portion of the first lighting element socket and a second section defining an interior bore dimensioned and arranged to enclose at least a lower, light emitting portion of the first lighting element,
wherein the cartridge is made from a material comprising a scented compound having a desired scent, the scented compound being present throughout the cartridge and having an elevated rate of vaporization from the material when the cartridge is in a heated state due to being in close proximity to one of an illuminated, heat producing lighting element and a discrete, resistive heating element, the elevated rate of vaporization being significantly greater than a reduced rate of vaporization of the scented compound from the material when the cartridge is not in the heated state and further wherein the cartridge includes the first and second sections, the interior bore of the first section being dimensioned and arranged to retain the upper portion of the first lighting element socket in a friction fitting relationship, whereby the cartridge may be removed and replaced after substantially all of the scented compound evaporates.
2. The assembly of claim 1, further including a second lighting element, a second lighting element socket electrically coupled to the electrical cord and dimensioned and arranged to retain and make mating electrical contract with the second lighting element, and a second fragrance releasing cartridge coupled to the second lighting element socket.
3. The assembly of claim 1, wherein the cartridge includes the second section, the second section defining an outer surface having a plurality of protuberances extending radially therefrom to provide an increased surface area for heat transfer and evaporation of the scented compound.
4. The assembly of claim 3, wherein the second section further defines an interior surface having a plurality of protuberances extending inwardly into the interior bore of the second section to thereby provide an increased surface area for heat transfer and evaporation of the scented compound.
5. The assembly of claim 1, wherein the cartridge includes the second section, the second section defining an interior surface having a plurality of protuberances extending inwardly into the interior bore of the second section to thereby provide an increased surface area for heat transfer and evaporation of the scented compound.
6. The assembly of claim 1, further including a housing having a shape representative of one of a pine tree, a candy cane, a gingerbread man, and another distinctive shape having a correspondingly distinct identifying aroma associated therewith, said housing including a translucent portion aligned with a mounting opening dimensioned and arranged to receive at least the upper section of the cartridge, whereby the first incandescent lighting element provides illumination of at least the translucent portion.
7. An article for use in a decorative illuminated assembly having an electrical cord terminated by at least one electrical connector, at least one incandescent lighting element, and at least one lighting element socket electrically coupled to the electrical cord and dimensioned and arranged to retain and make electrical contact with a corresponding incandescent lighting element, a fragrance releasing cartridge article comprising at least one of:
a first section defining a first interior bore dimensioned and arranged to receive and retain an upper portion of a lighting element socket; and
a second section defining a second interior bore dimensioned and arrange to enclose at least a lower, light emitting portion of a lighting element retained in a lighting element socket, wherein the cartridge is made from a material comprising a scented compound having a desired scent, the scented compound being present throughout the cartridge and having an elevated rate of vaporization from the material when the cartridge is in a heated state due to being in close proximity to one of an illuminated, heat producing lighting element and a discrete, resistive heating element, the elevated rate of vaporization being significantly greater than a reduced rate of vaporization of the scented compound from the material when the cartridge is not in the heated state, and further wherein the cartridge includes the first and second sections, the interior bore of the first section being dimensioned and arranged to retain the upper portion of the first lighting element socket in a friction fitting relationship, whereby the cartridge may be removed and replaced after substantially all of the scented compound evaporates.
8. The article of claim 7, the article including both the first section and the second section and wherein the first interior bore is axially aligned with the second interior bore.
9. The article of claim 8, wherein the first interior bore of the cartridge is dimensioned and arranged to retain the upper portion of a corresponding lighting element socket in a friction fitting relationship, whereby the cartridge may be removed and replaced.
10. The article of claim 8, wherein the second section of the fragrance releasing cartridge defines an outer surface having formed thereon a plurality of outwardly extending protuberances to provide an increased surface area for heat transfer and evaporation of the scented compound.
11. The article of claim 10, wherein the second section of the fragrance releasing cartridge further defines an interior surface having formed thereon a plurality of protuberances extending inwardly into the second interior bore to provide an increased surface area for heat transfer and evaporation of the scented compound.
12. The article of claim 8, wherein the second section of the fragrance releasing cartridge defines an interior surface having formed thereon a plurality of protuberances extending inwardly into the second interior bore to provide an increased surface area for heat transfer and evaporation of the scented compound.
13. The article of claim 8, further including a housing having a shape representative of one of a pine tree, a candy cane, and a gingerbread man, said housing including a translucent portion aligned with a mounting opening dimensioned and arranged to receive at least the upper section of the cartridge, whereby the first incandescent lighting element provides illumination of at least the translucent portion.
14. The article of claim 7, further including a thermal conductivity enhancer present in an amount sufficient to increase the thermal conductivity of the cartridge.
15. The article of claim 14, wherein the cartridge is fabricated from a translucent elastomeric material and wherein the thermal conductivity enhancer is a thermally conductive nanopowder.
16. A decorative light string assembly, comprising:
an electrical cord terminated by at least one electrical connector;
a plurality of lighting elements;
a plurality of lighting element sockets each electrically coupled to the electrical cord and dimensioned and arranged to retain and make mating electrical contact with a corresponding one of the plurality of lighting elements; and
a plurality of fragrance releasing cartridges each coupled to a corresponding one of the lighting element sockets, each said cartridge having at least one of a first section defining a first interior bore dimensioned and arranged to receive and retain an upper portion of a corresponding lighting element socket and a second section defining a second interior bore dimensioned and arranged to enclose at least a lower, light emitting portion of a corresponding lighting element, wherein each cartridge is made from a material comprising a scented compound having a desired scent, the scented compound being present throughout each cartridge and having an elevated rate of vaporization from the material when each cartridge is in a heated state due to being in close proximity to one of an illuminated lighting element and a heat-producing resistive element, the elevated rate of vaporization being significantly greater than a reduced rate of vaporization of the scented compound from the material when a cartridge is not in the heated state, wherein each cartridge includes both the first and second sections, the second section of each cartridge defining an outer surface having a plurality of protuberances extending radially therefrom to provide an increased surface area for heat transfer and evaporation of the scented compound.
17. The assembly of claim 16, wherein the cartridge includes the second section, the second section defining a plurality of protuberances extending inwardly into the second interior bore to thereby provide an increased surface area for heat transfer and evaporation of the scented compound.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method comprising:
obtaining, using a computing device, a query;
parsing, using the computing device, the query to identify that the query is associated with a mathematical function and is associated with a request for one or more documents;
determining, using the computing device and based on parsing the query, the mathematical function associated with the query;
identifying, using the computing device, transition points based on function values of the mathematical function for corresponding variable values of an independent variable in the mathematical function;
selecting, using the computing device, an initial graph range for the corresponding variable values of the independent variable based on a number of the identified transition points;
selecting, using the computing device, an initial graph domain for the function values based on the selected initial graph range;
providing, for presentation in a first section of a search results web page and using the computing device, the selected initial graph range and the selected initial graph domain for plotting the mathematical function in a graph; and
providing, for presentation in a second section of the search results web page, one or more selectable links to the one or more documents associated with the query,
the first section being different than the second section.
2. The method of claim 1, wherein the transition points include at least one point where:
a function value of the function values is zero,
a first derivative of the mathematical function is zero,
a second derivative of the mathematical function is zero, or
the second derivative exceeds a predefined value.
3. The method of claim 1, wherein the transition points include at least one point where the mathematical function has a vertical asymptote.
4. The method of claim 1, wherein the initial graph range includes all of the identified transition points.
5. The method of claim 1, wherein the initial graph range includes a number of the identified transition points between a minimum threshold number and a maximum threshold number.
6. The method of claim 1, wherein, when selecting the initial graph domain, the method includes:
calculating function values for corresponding variable values of the independent variable within the initial graph range; and
selecting the initial graph domain based on a minimum function value and a maximum function value within the calculated function values.
7. The method of claim 1, wherein, when selecting the initial graph range, the method includes:
determining whether the mathematical function is a predetermined function type; and
identifying, when the mathematical function is the predetermined function type, transition points having characteristics that depend on the predetermined function type.
8. The method of claim 1, wherein, when selecting the initial graph range, the method includes:
calculating function values for overlapping ranges of variable values for the independent variable;
determining transition points within the overlapping ranges; and
selecting the initial graph range from among the overlapping ranges based on a number of the transition points within the overlapping ranges.
9. The method of claim 8, further comprising:
calculating scores for the overlapping ranges,
wherein a score for a given overlapping range is based on the number of transition points occurring within the given overlapping range; and
selecting the initial graph range from among the overlapping ranges based on the calculated scores.
10. The method of claim 9, wherein the score for the given overlapping range is weighted based on corresponding variable values of the independent variable at the transition points.
11. A non-transitory computer readable storage medium storing instructions, the instructions comprising:
one or more instructions which, when executed by at least one processor, cause the at least one processor to:
receive a query;
parse the query to identify that the query is associated with a mathematical function and is associated with a request for one or more documents;
determine, based on parsing the query, the mathematical function associated with the query;
identify transition points based on function values of the mathematical function for corresponding variable values of an independent variable in the mathematical function;
select an initial graph range for the corresponding variable values of the independent variable based on a number of the identified transition points;
select an initial graph domain for the function values based on the selected initial graph range;
provide, for presentation in a first section of a search results web page, the selected initial graph range and the selected initial graph domain for plotting the mathematical function in a graph; and
provide, for presentation in a second section of the search results web page, one or more selectable links to the one or more documents associated with the query,
the first section being different than the second section.
12. The non-transitory computer readable storage medium of claim 11, wherein the transition points include at least one point where:
a function value of the function values is zero,
a first derivative of the mathematical function is zero,
a second derivative of the mathematical function is zero, or
the second derivative exceeds a predefined value.
13. The non-transitory computer readable storage medium of claim 11, wherein the transition points include at least one point where the mathematical function has a vertical asymptote.
14. The non-transitory computer readable storage medium of claim 11, wherein the initial graph range includes all of the identified transition points.
15. The non-transitory computer readable storage medium of claim 11, wherein the initial graph range includes a number of the identified transition points between a minimum threshold number and a maximum threshold number.
16. The non-transitory computer readable storage medium of claim 11, wherein the one or more instructions to select the initial graph domain include:
one or more instructions to calculate function values for corresponding variable values of the independent variable within the initial graph range; and
one or more instructions to select the initial graph domain based on a minimum function value and a maximum function value within the calculated function values.
17. The non-transitory computer readable storage medium of claim 11, wherein the one or more instructions to select the initial graph range include:
one or more instructions to determine whether the mathematical function is a predetermined function type; and
one or more instructions to identify, when the mathematical function is the predetermined function type, transition points having characteristics that depend on the predetermined function type.
18. The non-transitory computer readable storage medium of claim 11, wherein the one or more instructions to select the initial graph range include:
one or more instructions to calculate function values for overlapping ranges of variable values for the independent variable;
one or more instructions to determine transition points within the overlapping ranges; and
one or more instructions to select the initial graph range from among the overlapping ranges based on a number of the transition points within the overlapping ranges.
19. The non-transitory computer readable storage medium of claim 18, where the instructions further include:
one or more instructions to calculate scores for the overlapping ranges,
wherein a score for a given overlapping range is based on the number of transition points occurring within the given overlapping range; and
one or more instructions to select the initial graph range from among the overlapping ranges based on the calculated scores.
20. The non-transitory computer readable storage medium of claim 19, wherein the score for the given overlapping range is weighted based on corresponding variable values of the independent variable at the transition points.
21. A system comprising:
a memory to store instructions; and
one or more processors to execute the instructions to:
obtain a query;
parse the query to identify that the query is associated with a mathematical function and is associated with a request for one or more documents;
determine, based on parsing the query, the mathematical function associated with the query;
identify transition points based on function values of the mathematical function for corresponding variable values of an independent variable in the mathematical function;
select an initial graph range for the corresponding variable values of the independent variable based on a number of the identified transition points;
select an initial graph domain for the function values based on the selected initial graph range;
provide, for presentation in a first section of a search results web page, the selected initial graph range and the selected initial graph domain for plotting the mathematical function in a graph, and
provide, for presentation in a second section of the search results web page, one or more selectable links to the one or more documents associated with the query,
the first section being different than the second section.
22. The system of claim 21, wherein the transition points include at least one point where:
a function value of the function values is zero,
a first derivative of the mathematical function is zero,
a second derivative of the mathematical function is zero, or
the second derivative exceeds a predefined value.
23. The system of claim 21, wherein the transition points include at least one point where the mathematical function has a vertical asymptote.
24. The system of claim 21, wherein the initial graph range includes all of the identified transition points.
25. The system of claim 21, wherein the initial graph range includes a number of the identified transition points between a minimum threshold number and a maximum threshold number.
26. The system of claim 21, wherein the one or more processors, when selecting the initial graph domain, are further to:
calculate function values for corresponding variable values of the independent variable within the initial graph range; and
select the initial graph domain based on a minimum function value and a maximum function value within the calculated function values.
27. The system of claim 21, wherein the one or more processors, when selecting the initial graph range, are further to:
determine whether the mathematical function is a predetermined function type; and
identify, when the mathematical function is the predetermined function type, transition points having characteristics that depend on the predetermined function type.
28. The system of claim 21, wherein the one or more processors, when selecting the initial graph range, are further to:
calculate function values for overlapping ranges of variable values for the independent variable;
determine transition points within the overlapping ranges; and
select the initial graph range from among the overlapping ranges based on a number of the transition points within the overlapping ranges.
29. The system of claim 28, wherein the one or more processors are further to:
calculate scores for the overlapping ranges,
wherein a score for a given overlapping range is based on the number of transition points occurring within the given overlapping range; and
select the initial graph range from among the overlapping ranges based the calculated scores.
30. The system of claim 29, wherein the score for the given overlapping range is weighted based on corresponding variable values of the independent variable at the transition points.