Abstract: A size adjustable LED light system has a first and second light retainer that are configured as mirror images to retain a front LED light strip of variable heights and lengths. Also, each of the first and second light retainer form a side LED light receiver channel configured to receive a side LED light. The front extensions of each of the light retainers create a barrier between the front LED light strip and the side LED light, to enable different colors of light to be projected from the front and the two sides. The first and second light retainers have front panel channel for retaining a front panel of the front LED light strip and side panel channels for retaining a side panel over the respective side LED light or side LED light panel.

Abstract: Embodiments of a laser system having an extremely large number of small pulsed lasers for irradiating small targets in inertial confinement fusion experiments, high energy density physics experiments, and inertial fusion power plants is more flexible than existing laser systems. Embodiments facilitate finer control of critical features of laser pulses for inertial fusion, as well as significant reduction in development costs and expansion of the community involved in the research relative to existing laser systems. Embodiments produce smooth intensity profiles at the target, large bandwidth that is over two orders of magnitude greater than existing laser systems, and fine control over laser wavelengths, focal properties, temporal pulse shape, and illumination geometry. Properties of each of the small pulsed lasers are individually selectable.

Abstract: Embodiments of a laser system having an extremely large number of small pulsed lasers for irradiating small targets in inertial confinement fusion experiments, high energy density physics experiments, and inertial fusion power plants is more flexible than existing laser systems. Embodiments facilitate finer control of critical features of laser pulses for inertial fusion, as well as significant reduction in development costs and expansion of the community involved in the research relative to existing laser systems. Embodiments produce smooth intensity profiles at the target, large bandwidth that is over two orders of magnitude greater than existing laser systems, and fine control over laser wavelengths, focal properties, temporal pulse shape, and illumination geometry. Properties of each of the small pulsed lasers are individually selectable.

Abstract: A size adjustable LED light system has a first and second light retainer that are configured as mirror images to retain a front LED light strip of variable heights and lengths. Also, each of the first and second light retainer form a side LED light receiver channel configured to receive a side LED light. The front extensions of each of the light retainers create a barrier between the front LED light strip and the side LED light, to enable different colors of light to be projected from the front and the two sides. The first and second light retainers have front panel channel for retaining a front panel of the front LED light strip and side panel channels for retaining a side panel over the respective side LED light or side LED light panel.

Abstract: Embodiments of a laser system having an extremely large number of small pulsed lasers for irradiating small targets in inertial confinement fusion experiments, high energy density physics experiments, and inertial fusion power plants is more flexible than existing laser systems. Embodiments facilitate finer control of critical features of laser pulses for inertial fusion, as well as significant reduction in development costs and expansion of the community involved in the research relative to existing laser systems. Embodiments produce smooth intensity profiles at the target, large bandwidth that is over two orders of magnitude greater than existing laser systems, and fine control over laser wavelengths, focal properties, temporal pulse shape, and illumination geometry. Properties of each of the small pulsed lasers are individually selectable.

Abstract: Disclosed are methods and systems to encrypt/decrypt a data message using Geometric Algebra and Hensel encoding (i.e., finite p-adic arithmetic). The security key(s), message data, and ciphertext are all represented as Geometric Algebra multivectors where a sum of the coefficients of an individual multivector is equal to the numeric value of the corresponding message or security key. Various Geometric Algebra operations with the message and security key multivectors act to encrypt/decrypt the message data. Each coefficient of the security key and message multivectors is further Hensel encoded to provide additional confusion/diffusion for the encrypted values. The Geometric Algebra operations permit homomorphic operations for adding, subtracting, multiplication and division of ciphertext multivectors such that the resulting ciphertext, when decrypted, is equal to corresponding mathematical operations using the unencrypted values.

Abstract: Disclosed are methods and systems to conceal (encrypt) & recover (decrypt) a data message using Geometric Algebra using Modular Concealment (MC) between a first computing device and a second computing device over a network communication connection. The security key(s), message data, and ciphertext are all represented as Geometric Algebra multivectors. The MC concealment provides for both additive and multiplicative homomorphism. Further data representations are presented for multivector packing schemes including Clifford Eigenvalue Packing (CEP) and Complex Magnitude Squared Packing (CMSP). The CEP and CMSP data representations also provide support for additive and multiplicative homomorphism. To assist in security key exchange, a key exchange protocol is also presented for the creation and transfer of security key multivectors.

Abstract: Disclosed are methods and systems to provide distributed computation within a Fully Homomorphic Encryption (FHE) system by using g-adic properties to separate a ciphertext into multiple ciphertexts for each Hensel digit level. A number t of computation units may individually perform addition and/or multiplication of each Hensel digit level on each of the computation units and then reconstruct the resulting value from the result ciphertext of each computation unit using p-adic and g-adic operations. Accordingly, computation burdens may be distributed to several computation units.

Abstract: Disclosed are methods and systems to encrypt data with SomeWhat Homomorphic Encryption (SWHE) properties for submission to a distributed ledger/blockchain that allows further open operations retained in the distributed ledger/blockchain on the encrypted data that will be properly reflected when the encrypted result is decrypted by the data owner. The somewhat homomorphic properties include addition and scalar division. Also disclosed is an ability to update a secret key applied for a ciphertext such that a single piece of data may be provided on the distributed ledger/blockchain by a data owner to a new data owner without also exposing other data encrypted with the original secret key of the original data owner.

Abstract: Disclosed are methods and systems to encrypt/decrypt a data message using Geometric Algebra and Hensel encoding (i.e., finite p-adic arithmetic). The security key(s), message data, and ciphertext are all represented as Geometric Algebra multivectors where a sum of the coefficients of an individual multivector is equal to the numeric value of the corresponding message or security key. Various Geometric Algebra operations with the message and security key multivectors act to encrypt/decrypt the message data. Each coefficient of the security key and message multivectors is further Hensel encoded to provide additional confusion/diffusion for the encrypted values. The Geometric Algebra operations permit homomorphic operations for adding, subtracting, multiplication and division of ciphertext multivectors such that the resulting ciphertext, when decrypted, is equal to corresponding mathematical operations using the unencrypted values.

Abstract: A sliding member for vehicular suspension includes a wear resistant layer having appropriate mechanical strength and high designability on its outer peripheral sliding face and a method for producing the same. On an outer peripheral sliding face of the sliding member for vehicular suspension, a colored wear resistant layer formed by an ion plating method and having a film thickness of 0.75 ?m or more and 10 ?m or less is included; and in the wear resistant layer, a dark blue titanium oxide layer, a titanium intermediate layer, and a colored titanium oxide layer are laminated in this order from the inner peripheral side toward the outer peripheral side.

Abstract: Disclosed are methods and systems to encrypt and decrypt a data message using Geometric Algebra. The encrypt operation performed on a source computing device uses the geometric product (Clifford Product) of a multivector created from plain text/data of the data message with one or more other multivectors that carry encryption keys, the identity of the source and/or other data-centric information. The source computing device sends the encrypted message to a destination computing device. The decrypt operation performed on the destination computing devices recovers the original message multivector, and ultimately the original data message by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.

Abstract: A sliding member for vehicular suspension includes a wear resistant layer having appropriate mechanical strength and high designability on its outer peripheral sliding face and a method for producing the same. On an outer peripheral sliding face of the sliding member for vehicular suspension, a colored wear resistant layer formed by an ion plating method and having a film thickness of 0.75 ?m or more and 10 ?m or less is included; and in the wear resistant layer, a dark blue titanium oxide layer, a titanium intermediate layer, and a colored titanium oxide layer are laminated in this order from the inner peripheral side toward the outer peripheral side.

Abstract: The present disclosure includes both systems and methods for introducing variety into search results of non-stock consumer goods. This variety is introduced by recording the common characteristics of non-stock consumer goods in a database and tracking the number of goods with a common characteristic that would be displayed on a webpage. If too many of one type of good would be displayed on a webpage, alternative goods are displayed in place of the additional goods with common characteristics, even if these goods are more relevant to the search performed by a user. In this way, consumers can efficiently be presented with both relevant and alternative non-stock consumer goods, saving consumers' time and using less computing power.

Abstract: Disclosed are methods and systems for encrypting numeric messages using Geometric Algebra on at least one source device and then storing and sorting the encrypted messages on an intermediary system without decrypting the encrypted numeric messages on the intermediary system and/or on a sort request device requesting the sort. Both the intermediary and sort request devices/systems do not need to have knowledge of the encryption security keys. A sort result (sorted group of cryptotext multivectors) may be sent to a destination device. The sorted encrypted data may be decrypted and kept in sorted order on the destination device. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data with one or more other multivectors that carry encryption keys. Decrypt operations decrypt encrypted data by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.

Abstract: Disclosed are methods and systems for encrypting numeric messages using Geometric Algebra on at least one source device and then storing and searching the encrypted messages on an intermediary system without decrypting the encrypted numeric messages on the intermediary system and/or on a search request device requesting the search. Both the intermediary and search request devices/systems do not need to have knowledge of the encryption security keys. A search result (FOUND/NOT-FOUND) may be sent to a destination device. The FOUND encrypted data, as well as other encrypted data linked to the FOUND encrypted data, may be sent to a destination device and decrypted. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data with one or more other multivectors that carry encryption keys. Decrypt operations decrypt encrypted data by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.

Abstract: Provided is a semi-continuous fermentation method of a rhamnolipid producing microorganism to produce rhamnolipids. The fermentation may be run as a batch process but at the end of the fermentation, at least about 70% of the fermentation medium comprising one or more rhamnolipids is drawn out and the new culture medium (feedstock) is fed in as a replacement. This process may be repeated for at least about one month without having to sacrifice RL yield and titer. It allows the fermenter to be utilized at a higher capacity with less downtime for clean-up compared to batch and fed batch fermentation strategies.

Abstract: Disclosed are methods and systems for encrypting a numeric message using Geometric Algebra on a source computing device, performing scalar-vector multiplication on the encrypted numeric message and an unencrypted scalar data value to get an encrypted scalar multiplicative result without decrypting the encrypted numeric message on an intermediary computing system that does not have knowledge of the encryption security keys, and decrypting using Geometric Algebra the encrypted scalar multiplicative result on a destination computing device such that the decrypted result is equal to multiplication of the unencrypted numeric message and the scalar data value. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data of the numeric data message with one or more other multivectors that carry encryption keys.

Abstract: Disclosed are methods and systems to encrypt and decrypt a data message using Geometric Algebra. The encrypt operation performed on a source computing device uses the geometric product (Clifford Product) of a multivector created from plain text/data of the data message with one or more other multivectors that carry encryption keys, the identity of the source and/or other data-centric information. The source computing device sends the encrypted message to a destination computing device. The decrypt operation performed on the destination computing devices recovers the original message multivector, and ultimately the original data message by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.