All The Claims

1. A pneumatic tire provided with a tread pattern on which a plurality of blocks are formed with circumferential grooves which extend along a circumferential direction of the tire and lateral grooves which traverse the circumferential grooves,
wherein the lateral groove disposed between the blocks on the endmost tread edge region has a depth from 10 to 50% of a depth of the circumferential groove to be traversed and has a groove bottom concave portion whose both ends in a longitudinal direction are disposed inside the groove bottom, and a width of the groove bottom concave portion, which is determined on the basis of the bottom plane of the groove bottom, is from 25 to 45% of a groove width of the lateral groove.
2. The pneumatic tire according to claim 1, wherein a depth of the deepest part of the groove bottom concave portion is from 10 to 25% of the depth of the circumferential groove.
3. The pneumatic tire according to claim 1, wherein the block on the endmost tread edge region has a land portion sipe, which extends subparallel to the lateral groove disposed between the blocks and bends on the median side, and one end of the land portion sipe closes at a vicinity of the outer end of the block, while the other end thereof is open to the lateral groove.
4. The pneumatic tire according to claim 1, wherein the grooves in the circumferential direction of the tire are composed of three circumferential grooves, the lateral groove disposed between these circumferential grooves has a depth from 40 to 70% of a depth of the circumferential groove and has a groove bottom sipe on the groove bottom of the lateral groove, and both ends of the groove bottom sipe are open.

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 substituted adamantane of Formula (I) or (II):
wherein
X represents a halogen atom;
Y is a C1-C10 alkyl group, a halogenated C1-C10 alkyl group, a halogen atom or a hetero atom-containing group;
R1 and R2 represents, independently, hydrogen, a halogen atom, a C1-C10 alkyl group or a halogenated C1-C10 alkyl group;
R3 and R4 represent, independently, hydrogen, a C1-C10 alkyl group, or a C1-C10 halogenated alkyl group,
wherein R3 and R4 cannot both be hydrogen in Formula (I);
wherein, in the formula (I), m represents an integer of 0 to 15, and n represents an integer of 1 to 10;
wherein, in the Formula (II), m represents an integer of 1 to 15.
2. A substituted adamantane selected from the group consisting of
wherein
X represents a halogen atom;
Y is a C1-C10 alkyl group, a halogenated C1-C10 alkyl group, a halogen atom or a hetero atom-containing group;
R1 and R2 represent, independently, hydrogen, a halogen atom, a C1-C10 alkyl group or a halogenated C1-C10 alkyl group;
R3 and R4 represent, independently, hydrogen, a C1-C10 alkyl group, or a C1-C10 halogenated alkyl group,
wherein R3 and R4 cannot both be hydrogen in Formulae (Ia-If);
wherein, in the formulae (Ia-If), m represents an integer of 0 to 13, and n represents an integer of 1 to 10;
wherein, in the Formula (IIa-IIe), m represents an integer of 1 to 13.
3. A process for producing the substituted adamantane of claim 1, comprising
reacting an alcohol comprising an adamantyl group represented by Formula (III) or (IV):
wherein in Formula (III), n represents an integer of 1 to 10;
with a carbonyl compound represented by Formula (V):
and at least one hydrogen halide gas; wherein R3 and R4 in Formula (V) are not both hydrogen when the carbonyl compound of formula (V) is reacted with the adamantyl group of Formula (III), and wherein m represents an integer of 1 to 13.

1. A digital signature verification apparatus comprising:
a memory to store a finite field Fq and a polynomial of a three-dimensional manifold A(x, y, s, t) defined as having degrees of freedom of three dimensions of a set of solutions of simultaneous equations, which is expressed by an x-coordinate, a y-coordinate, a parameter s, and a parameter t and is defined on the finite field Fq;
a processor configured to;
input a message m;
input a digital signature Ds: (Ux(t), Uy(t), t) corresponding to the message m, the digital signature being a curve on a section D(ux(s, t), uy(s, t), s, t) which is one of surfaces of the three-dimensional manifold A(x, y, s, t), the x-coordinate and y-coordinate of the section being expressed by functions of the parameter t, the digital signature being generated by using the section as a secret key;
calculate a hash value of the message m;
generate a hash value polynomial by embedding the hash value in a 1-variable polynomial for the parameter t defined on the finite field Fq;
calculate an algebraic surface X(x, y, t) corresponding to the hash value by substituting the hash value polynomial in the parameter s of the polynomial stored in the memory; and
verify authenticity of the message and the digital signature by substituting a function Ux(t) representing the x-coordinate of the digital signature and a function Uy(t) representing the y-coordinate of the digital signature in an x-coordinate and a y-coordinate, respectively, of the algebraic surface X(x, y, t).
2. A digital signature verification method including:
storing, in a memory, a finite field Fq and a polynomial of a three-dimensional manifold A(x, y, s, t) defined as having degrees of freedom of three dimensions of a set of solutions of simultaneous equations, which is expressed by an x-coordinate, a y-coordinate, a parameter s, and a parameter t and is defined on the finite field Fq;
inputting a message m;
inputting a digital signature Ds: (Ux(t), Uy(t), t) corresponding to the message m, the digital signature being a curve on a section D(ux(s, t), uy(s, t), s, t) which is one of surfaces of the three-dimensional manifold A(x, y, s, t), the x-coordinate and y-coordinate of the section being expressed by functions of the parameter t, the digital signature being generated by using the section as a secret key
calculating a hash value of the message m;
generating a hash value polynomial by embedding the hash value in a 1-variable polynomial for the parameter t defined on the finite field Fq;
calculating an algebraic surface X(x, y, t) corresponding to the hash value by substituting the hash value polynomial in the parameter s of the polynomial stored in the memory; and
verifying authenticity of the message and the digital signature by substituting a function Ux(t) representing the x-coordinate of the digital signature and a function Uy(t) representing the y-coordinate of the digital signature in an x-coordinate and a y-coordinate, respectively, of the algebraic surface X(x, y, t).
3. A digital signature verification program stored on a non-transitory computer readable medium, the program including:
a first program instruction which when executed by a computer processor, causes storing, in a memory, a finite field Fq and a polynomial of a three-dimensional manifold A(x, y, s, t) defined as having degrees of freedom of three dimensions of a set of solutions of simultaneous equations, which is expressed by an x-coordinate, a y-coordinate, a parameter s, and a parameter t and is defined on the finite field Fq;
a second program instruction which when executed by the computer processor, causes inputting a message m;
a third program instruction which when executed by the computer processor, causes inputting a digital signature Ds: (Ux(t), Uy(t), t) corresponding to the message m, the digital signature being a curve on a section D(ux(s, t), uy(s, t), s, t) which is one of surfaces of the three-dimensional manifold A(x, y, s, t), the x-coordinate and y-coordinate of the section being expressed by functions of the parameter t, the digital signature being generated by using the section as a secret key;
a fourth program instruction which when executed by the computer processor, causes calculating a hash value of the message m;
a fifth program instruction which when executed by the computer processor, causes generating a hash value polynomial by embedding the hash value in a 1-variable polynomial for the parameter t defined on the finite field Fq;
a sixth program instruction which when executed by the computer processor, causes calculating an algebraic surface X(x, y, t) corresponding to the hash value by substituting the hash value polynomial in the parameter s of the polynomial stored in the memory; and
a seventh program instruction which when executed by the computer processor, causes verifying authenticity of the message and the digital signature by substituting a function Ux(t) representing the x-coordinate of the digital signature and a function Uy(t) representing the y-coordinate of the digital signature in an x-coordinate and a y-coordinate, respectively, of the algebraic surface X(x, y, t).

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 fiber-optic transceiver module comprising
A fiber-optic transmitter;
A first fiber-optic receiver;
A second fiber-optic receiver;
A digital multiplexer;
A controller to control the multiplexer.
2. A fiber-optic transmitter as in claim 1, generating a modulated optical power in response to a digital input.
3. A first fiber-optic receiver as in claim 1, generating a digital output in response to modulated optical power at its optical input.
4. A second fiber-optic receiver as in claim 1, generating a digital output in response to modulated optical power at its optical input.
5. A digital multiplexer as in claim 1, to select and route data from either the first fiber-optic receiver, or from the second fiber-optic receiver, to the transceiver’s output.
6. A controller as in claim 1, to control the multiplexer.
7. An optical power splitter, not inside the fiber-optic transceiver module, to receive optical power from the transmitter as in claim 1, and produce two reduced power copies of the received optical power, and transfer these copies of the input optical power to two fiber-optic cables.
8. A fiber-optic transceiver module comprising
A fiber-optic transmitter;
A fiber-optic power splitter
A first fiber-optic receiver;
A second fiber-optic receiver;
A digital multiplexer;
A controller to control the multiplexer.
9. A fiber-optic transmitter as in claim 8, generating a modulated optical power in response to a digital input.
10. A fiber-optic receiver as in claim 8, generating a digital output in response to modulated optical power at its optical input.
11. A second fiber-optic receiver as in claim 8, generating a digital output in response to modulated optical power at its optical input.
12. A digital multiplexer as in claim 8, to select and route data from either the first fiber-optic receiver, or from the second fiber-optic receiver, to the transceiver’s output
13. A controller as in claim 8, to control the multiplexer.
14. An optical power splitter to receive optical power from the transmitter as in claim 8, and to produce two reduced power copies of the received optical power, and to transfer these copies of the input optical power to two fiber-optic ports of the transceiver module.
15. A fiber-optic transceiver module comprising
A first fiber-optic transmitter;
A second fiber-optic transmitter;
A first fiber-optic receiver;
A second fiber-optic receiver;
A digital multiplexer;
A controller to control the multiplexer.
16. A first fiber-optic transmitter as in claim 15, generating a modulated optical power in response to a digital input.
17. A second fiber-optic transmitter as in claim 15, generating a modulated optical power in response to a digital input, wherein the digital input to the second transmitter is identical to the digital input to the first fiber-optic transmitter, and further wherein both the first and the second fiber-optic transmitters may transmit simultaneously.
18. A first fiber-optic receiver as in claim 15, generating a digital output in response to modulated optical power at its optical input.
19. A second fiber-optic receiver as in claim 15, generating a digital output in response to modulated optical power at its optical input.
20. A digital multiplexer as in claim 15, to select and route data from either the first fiber-optic receiver or from the second fiber-optic receiver to the transceiver’s output.
21. A controller as in claim 15, to control the multiplexer.
22. A fully redundant fiber-optic communication link comprising of
A first fiber-optic transceiver module as in claim 1;
A second fiber-optic transceiver module as in claim 1;
A first pair of fiber-optic cables;
A second pair of fiber-optic cables;
A first optical power splitter as in claim 7;
A second optical power splitter as in claim 7.
23. A fiber-optic transceiver as in claim 22 comprising of
A fiber-optic transmission port;
A first fiber-optic reception port;
A second fiber-optic reception port;
A single digital data input port;
A single digital data output port.
24. A first pair of fiber-optic cables as in claim 22, wherein the first fiber-optic cable of the first pair conveys optical power in a first direction into the first receiving port of the second fiber-optic transceiver, and wherein the second fiber-optic cable of the first pair conveys optical power in a second direction into the first receiving port of the first fiber-optic transceiver.
25. A second pair of fiber-optic cables as in claim 22, wherein the first fiber-optic cable of the second pair conveys optical power in a first direction into the second receiving port of the second fiber-optic transceiver, and wherein the second fiber-optic cable of the second pair conveys optical power in a second direction into the second receiving port of the first fiber-optic transceiver.
26. A first optical power splitter as in claim 22, wherein an input port of the optical power splitter connects via a fiber-optic cable to the optical transmission port of the first fiber-optic transceiver, and wherein the first output port of the first optical power splitter connects to the first fiber-optic cable of the first pair of cables, and further wherein the second output port of the first optical power splitter connects to the first fiber-optic cable of the second pair of fiber-optic cables.
27. A second optical power splitter as in claim 22, wherein an input port of the optical power splitter connect via a fiber-optic cable to the optical transmission port of the second fiber-optic transceiver, and wherein the first output port of the second optical power splitter connects to the second fiber-optic cable of the first pair of cables, and further wherein the second output port of the second optical power splitter connects to the second fiber-optic cable of the second pair of fiber-optic cables.
28. A fully redundant fiber-optic communication link comprising of
A first fiber-optic transceiver module as in claim 8;
A second fiber-optic transceiver module as in claim 8;
A first pair of fiber-optic cables;
A second pair of fiber-optic cables;
A first optical power splitter as in claim 7;
A second optical power splitter as in claim 7.
29. A fiber-optic transceiver as in claim 28 comprising of
A first fiber-optic transmission port;
A second fiber-optic transmission port;
A first fiber-optic reception port;
A second fiber-optic reception port;
A single digital data input port;
A single digital data output port.
30. A first pair of fiber-optic cables as in claim 28, wherein the first end of first fiber-optic cable of the first pair connects to the first optical transmission port of the first fiber-optic transceiver, and wherein the second end of the first fiber-optic cable of the first pair of fiber-optic cables connects to the first optical reception port of the second fiber-optic transceiver.
31. A first pair of fiber-optic cables as in claim 28, wherein the second end of the second fiber-optic cable of the first pair connects to the first optical transmission port of the second fiber-optic transceiver, and wherein the first end of the second fiber-optic cable of the first pair of fiber-optic cables connects to the first optical reception port of the first fiber-optic transceiver.
32. A second pair of fiber-optic cables as in claim 28, wherein the first end of the first fiber-optic cable of the second pair connects to the second optical transmission port of the first fiber-optic transceiver, and wherein the second end of the first fiber-optic cable of the second pair of fiber-optic cables connects to the second optical reception port of the second fiber-optic transceiver.
33. A second pair of fiber-optic cables as in claim 28, wherein the second end of the second fiber-optic cable of the second pair connects to the second optical transmission port of the second fiber-optic transceiver, and wherein the first end of the second fiber-optic cable of the second pair of fiber-optic cables connects to the second optical reception port of the first fiber-optic transceiver.
34. A fully redundant fiber-optic communication link comprising of
A first fiber-optic transceiver module as in claim 15;
A second fiber-optic transceiver module as in claim 15;
A first pair of fiber-optic cables;
A second pair of fiber-optic cables.
35. A fiber-optic transceiver as in claim 34 comprising of
A first fiber-optic transmission port;
A second fiber-optic transmission port;
A first fiber-optic reception port;
A second fiber-optic reception port;
A single digital data input port;
A single digital data output port.
36. A first pair of fiber-optic cables as in claim 34, wherein the first end of first fiber-optic cable of the first pair connects to the first optical transmission port of the firs fiber-optic transceiver, and wherein the second end of the first fiber-optic cable of the first pair of fiber-optic cables connects to the first optical reception port of the second fiber-optic transceiver.
37. A first pair of fiber-optic cables as in claim 34, wherein the second end of second fiber-optic cable of the first pair connects to the first optical transmission port of the second fiber-optic transceiver, and wherein the first end of the second fiber-optic cable of the first pair of fiber-optic cables connects to the first optical reception port of the first fiber-optic transceiver.
38. A second pair of fiber-optic cables as in claim 34, wherein the first end of the first fiber-optic cable of the second pair connects to the second optical transmission port of the first fiber-optic transceiver, and wherein the second end of the first fiber-optic cable of the second pair of fiber-optic cables connects to the second optical reception port of the second fiber-optic transceiver.
39. A second pair of fiber-optic cables as in claim 34, wherein the second end of the second fiber-optic cable of the second pair connects to the second optical transmission port of the second fiber-optic transceiver, and wherein the first end of the second fiber-optic cable of the second pair of fiber-optic cables connects to the second optical reception port of the first fiber-optic transceiver.
40. A fully redundant fiber-optic communication link wherein the failure of a transceiver, or a repeater or any other intermediary component on one of the two redundant communication channels does not cause interruption of communication, allowing uninterrupted communication through the alternate communication channel.
41. A fully redundant fiber-optic communication link as in claim 40, wherein the decisions on switching communication channels in case of failure in one communication channel, or switching back upon recovery of the failed channel, can be controlled automatically or by administrative control.
42. A fully redundant fiber-optic communication link as in claim 40, wherein the selection of the primary communication channel can be done by the communication network administrator.