Cyclic Codes a cyclic code is a linear block code where if c is a codeword, so are all cyclic shifts of c E.g., 1000, 110, 101,011 is a cyclic code Cyclic codes can be dealt with in the very same way as all other lbc s Generator and parity check matrix can be found a cyclic code can be completely described by a generator string G All codewords are multiples of the generator string In practice, cyclic codes are often used for error detection(CRc) Used for packet networks When an error is detected by the received, it requests retransmission

Modulation Representing digital signals as analog waveforms Baseband signals Signals whose frequency components are concentrated around zero Passband signals Signals whose frequency components are centered at some frequency fc away from zero Baseband signals can be converted to passband signals through modulation Multiplication by a sinusoid with frequency fc Eytan Modiano

Noise is additional\unwanted \signal that interferes with the transmitted signal Generated by electronic devices The noise is a random process Each\sample \ of n(tis a random variable Typically, the noise process is modeled as\Additive White Gaussian noise”(AWGN) White: Flat frequency spectrur Gaussian noise distribution

Channel Coding When transmitting over a noisy channel, some of the bits are received with errors Example: Binary Symmetric Channel (BSc) Pe= probability oferror Q: How can these errors be removed? A: Coding: the addition of redundant bits that help us determine what was sent with greater accuracy

1965年发 Kalamazoo现斑岩铜矿 发现 Escondida斑岩铜矿 发现 JA and Maggie Creek sites in British Columbia和 Vekol Hills in Arizona 发现秘鲁 Pierina金银矿床,卖了11亿加元

食品冷藏链是指易腐食品在生产、贮藏、运输、销售、直至消费前的各个环节中始终处于规定的低温环境下，以保证食品质量，减少食品损耗的一项系统工程

家畜环境卫生学是一门综合性的学科,涉及的范围极广,它必须以物理、化学、微 生物学、生理学、生态学、病理学、畜牧机械、畜牧系统工程等基础科学为基础;同时又 与饲养学、繁殖学、育种学、牧场经营管理学、动物医学等有密切联系

accelerations account for non-central forces(drag, thrust, etc. X-axis in zenith, y-axis in frames velocity, and z-axis in transverse directions 8 Free orbit solution where 'A and 'B' are lengths and'a andB are phase angles

家畜环境卫生是一门综合性的学科,涉及的范围极广,它必须以物理、化学、微生 物学、生理学、生态学、病理学、畜牧机械、畜牧系统工程等基础科学为基础:同时又与 饲养学、繁殖学、育种学、牧场经营管理学、动物医学等有密切联系

Was sind,, Axiome: eigentlich Behauptungen. Wenn es gelingt, aus einer beschrankten Anzahl solcher Axiome\ einen in sich abgeschlosse- nen Bereich des Denkens zu schaffen( in der Philosophie und in etwas erzwungener Form auch in der Informatik als Onthologie-die Lehre des,,Seins\ bezeichnet). Dann kann man in diesem Bereich im Rahmen der Axiome ,spazieren denken\ Ein Beispiel hierfur ist die analytische